If you're seeing this message, it means we're having trouble loading external resources on our website. Show If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Hello, and welcome to this Mometrix video on specific heat capacity—a constant that relates heat transfer to changes in temperature. Temperature is directly related to the average translational kinetic energy of the atoms or molecules in a system. Basically, the faster and heavier the particles are, the higher the temperature. The units for temperature are degrees Celsius and Kelvin (remember, 0 degrees Celsius = 273 Kelvin, but 1 degree Celsius has the same magnitude as 1 Kelvin). Conversely, heat is measured in joules and is the energy transferred between systems at different temperatures that are in contact. Because heat is the transfer of energy, it is known as a process quantity. When heat is absorbed or released by a system, the temperature changes. How much the temperature changes depends on the substance, and specifically, the specific heat capacity of that substance. Let’s look at an example. Let’s say we have 47.8 grams of water at 35ºC and we put it on the stove. We turn on the stove and transfer 1,000 joules of heat to our water and the temperature rises to 40ºC. In other words, it took 1,000 joules of heat to raise 47.8 grams of water by 5ºC. That’s kind of a mouthful and seems oddly specific in terms of quantities. This is where specific heat capacity, notated as \(c\), comes into play. It’s a standard quantity and is the amount of heat required to raise 1 gram of a substance by 1 degree Celsius. With some simple division, we can derive the specific heat capacity of water from our hypothetical cup of water.
From this, we know now that it takes 4.184 joules to raise the temperature of 1 gram of water by 1 degree Celsius—that’s the specific heat capacity of water. This is really helpful to scientists because once determined, the specific heat capacity can be used to calculate the heat absorbed or released by a system simply by measuring the temperature change and mass. Let’s try that out. Let’s look at a new cup of water, let’s say a mug of 350 grams that’s boiling. The water starts at 100ºC and cools down to 90ºC. We want to know how much heat was released from the water to the surrounding environment. Since we know the specific heat capacity of water is 4.184 joules per gram Kelvin, we simply need to rearrange our previous equation to solve for \(q\) (the heat released).
Since we knew the specific heat capacity of water, calculating the heat released from the system was easy! Note here that the negative sign simply tells us that the system (the mug of water) released heat to the surrounding system rather than absorbed it. Now that we’ve defined specific heat capacity and demonstrated how it can be used to calculate the heat transferred from or to a system, let’s look at why the specific heat capacity changes between substances. For example, the specific heat capacity of ethanol is 2.18 joules per gram Kelvin, almost half of water. If we have one gram of water and one gram of ethanol both at 0ºC, it would take 4.18 joules of heat to raise the temperature of water to 1ºC, and only 2.18 joules for ethanol. The liquids reach the same temperature but require different amounts of heat. Why? Remember, to increase the temperature, we need to increase the average translational kinetic energy of the molecules (make the molecules move faster). But the internal energy of a substance is more than just the translational kinetic energy, it also includes potential energy from intermolecular interactions. When heat is transferred to a system, it is distributed amongst the kinetic and potential energies. So, if a system has more potential energy, a smaller proportion of the transferred heat is distributed to the kinetic energy, yielding a smaller increase in temperature. To better understand this concept, let’s look at water and ethanol again. In water, there is a complex network of hydrogen bonds between the molecules. Those interactions are part of the potential energy and need to be overcome, or broken, to increase the average translational kinetic energy. So, when we heat water, some of that energy is used to break up the hydrogen bonding network instead of increasing the kinetic energy, resulting in a large specific heat capacity. Conversely, in ethanol, there are fewer hydrogen bonds per molecule, or less potential energy, and therefore a larger proportion of the heat transferred is used to increase the average kinetic energy, which results in a smaller specific heat capacity. ReviewOkay, let’s wrap up with a review. First, we reviewed the scientific definitions of temperature and heat and related them using specific heat capacity. Using water as an example, we showed how once we know the specific heat capacity, it is quite easy to determine the heat transferred from or to a system. And finally, we considered from a microscopic view why substances have different specific heat capacities. Thanks for watching and happy studying! Specific heat capacity refers to the amount of energy or heat required to increase the temperature of 1 gram of a substance by one degree Celsius. A key characteristic of water is its high specific heat capacity. Water has to absorb 4,184 Joules of heat, or 1 calorie, to increase in temperature of 1 kilogram of water by 1 degree Celsius. The units often expressed for specific heat capacity are J/(g×C) or J/(kg×C). Heat capacity, also known as thermal mass, refers to the amount of heat energy require to raise the temperature of an object, and is measure in Joules per Kelvin or Joules per degree Celsius. Specific heat capacity, also known as specific heat, is the heat capacity per unit mass.
The SI-unit of heat - or energy - is joule (J). With temperature difference Other units used to quantify heat are the British Thermal Unit - Btu (the amount of heat to raise 1 lb of water by 1oF) and the Calorie (the amount of heat to raise 1 gram of water by 1oC (or 1 K)).
A calorie is defined as the amount of heat required to change the temperature of one gram of liquid water by one degree Celsius (or one degree Kelvin).
Heat Flow (Power)Heat-transfer as result of temperature difference alone is referred to as heat flow. The SI units for heat flow is J/s or watt (W) - the same as power. One watt is defined as 1 J/s. Specific EnthalpySpecific Enthalpy is a measure of the total energy in a unit mass. The SI-unit commonly used is J/kg or kJ/kg. The term relates to the total energy due to both pressure and temperature of a fluid (such as water or steam) at any given time and condition. More specifically enthalpy is the sum of internal energy and work done by applied pressure. Heat CapacityHeat Capacity of a system is
Specific HeatSpecific heat (= specific heat capacity) is the amount of heat required to change temperature of one mass unit of a substance by one degree. Specific heat may be measured in J/g K, J/kg K, kJ/kg K, cal/gK or Btu/lboF and more. Never use tabulated values of heat capacity without checking the unites of the actual values!
Specific heat for common products and materials can be found in the Material Properties section. Specific Heat - Constant PressureThe enthalpy - or internal energy - of a substance is a function of its temperature and pressure. The change in internal energy with respect to change in temperature at fixed pressure is the Specific Heat at constant pressure - cp. Specific Heat - Constant VolumeThe change in internal energy with respect to change in temperature at fixed volume is the Specific Heat at constant volume - cv. Unless the pressure is extremely high the work done by applied pressure on solids and liquids can be neglected, and enthalpy can be represented by the internal energy component alone. Constant-volume and constant-pressure heats can be said to be equal. For solids and liquids
The specific heat represents the amount of energy required to raise 1 kg of substance by 1oC (or 1 K), and can be thought of as the ability to absorb heat. The SI units of specific heats are J/kgK (kJ/kgoC). Water has a large specific heat of 4.19 kJ/kgoC compared to many other fluids and materials.
Amount of Heat Required to Rise TemperatureThe amount of heat needed to heat a subject from one temperature level to an other can be expressed as:
Example Heating Water Consider the energy required to heat 1.0 kg of water from 0 oC to 100 oC when the specific heat of water is 4.19 kJ/kgoC:
WorkWork and energy are from a technical viewpoint the same entity - but work is the result when a directional force (vector) moves an object in the same direction. The amount of mechanical work done can be determined by an equation derived from Newtonian mechanics
Work can also be described as the product of the applied pressure and the displaced volume:
Example - Work done by a ForceThe work done by a force 100 N moving a body 50 m can be calculated as W = (100 N) (50 m) = 5000 (Nm, J) The unit of work is joule, J, which is defined as the amount of work done when a force of 1 newton acts for a distance of 1 m in the direction of the force.
Example - Work due to Gravitational ForceThe work done when lifting a mass of 100 kg an elevation of 10 m can be calculated as W = Fg h = m g h = (100 kg) (9.81 m/s2) (10 m) = 9810 (Nm, J) where Fg = force of gravity - or weight (N) g = acceleration of gravity 9.81 (m/s2) h = elevation (m) In imperial units a unit work is done when a weight of 1 lbf (pound-force) is lifted vertically against gravity through a distance of 1 foot. The unit is called lb ft. An object with mass 10 slugs is lifted 10 feet. The work done can be calculated as W = Fg h = m g h = (10 slugs) (32.17405 ft/s2) (10 feet) = 3217 lbf ft Example - Work due to Change in VelocityThe work done when a mass of 100 kg is accelerated from a velocity of 10 m/s to a velocity of 20 m/s can be calculated as W = (v22 - v12) m / 2 = ((20 m/s)2 - (10 m/s)2) (100 kg) / 2 = 15000 (Nm, J) where v2 = final velocity (m/s) v1 = initial velocity (m/s) EnergyEnergy is the capacity to do work (a translation from Greek-"work within"). The SI unit for work and energy is the joule, defined as 1 Nm. Moving objects can do work because they have kinetic energy. ("kinetic" means "motion" in Greek). The amount of kinetic energy possessed by an object can be calculated as
The energy of a level position (stored energy) is called potential energy. This is energy associated with forces of attraction and repulsion between objects (gravity). The total energy of a system is composed of the internal, potential and kinetic energy. The temperature of a substance is directly related to its internal energy. The internal energy is associated with the motion, interaction and bonding of the molecules within a substance. The external energy of a substance is associated with its velocity and location, and is the sum of its potential and kinetic energy. |
What is defined as the amount of heat needed to raise the temperature of 1 gram of the substance by 1k or 1c?
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