Heat Capacity Of An Ideal Gas.pptx

Discussion about Heat Capacity Of An Ideal Gas with 2 examples given

1. HEAT CAPACITY OF AN IDEAL GAS

2. Specific Heat The specific heat capacity of an object is the amount of energy that is required to raise the temperature of one gram of substance on one degree Celsius. 𝑸 = 𝒎𝒄∆𝑻 Molar Heat Capacity is the amount of heat to raise the temperature of a mole of a substance . 𝑸 = 𝒏𝑪∆𝑻 REVIEW

3. HEAT CAPACITY OF AN IDEAL GAS The specific heat or molar heat capacity of a substance depends on the conditions under which the heat is added. The heat capacity of a gas is usually measured in a closed container under constant-volume conditions. The corresponding heat capacity is the molar heat capacity at constant volume, denoted by 𝐶 v Heat capacity measurements for solids and liquids are usually carried out under constant atmospheric pressure, and we call the corresponding heat capacity the molar heat capacity at constant pressure, 𝐶 p

4. MEASURING MOLAR HEAT CAPACITY Constant Volume Constant Pressure In a constant-volume temperature increase, the system does no work, and the change in internal energy equals the heat added 𝑸.   In constant-pressure temperature increase, volume must increase, so pressure remains constant.

5. pV -Diagram It shows the relation of 𝐶 p and 𝐶 v Raising the temperature of an ideal gas from T 1 to T 2 by a constant-volume or a constant-pressure process. For an ideal gas, U depends only on T, so ∆U is the same for both processes. But for the constant-pressure process, more heat Q must be added to both increase U and do work W. Hence 𝐶 p > C V .

6. RELATING 𝑪 𝒑 AND 𝑪 𝑽 FOR AN IDEAL GAS For constant volume :   For constant pressure : 𝒅𝑸 = 𝒏𝑪 𝒑 𝒅𝑻
𝒅𝑾 = 𝒑𝒅𝑽 = 𝒏𝑹𝒅𝑻
𝒏𝑪 𝒑 𝒅𝑻 = 𝒏𝑪 𝑽 𝒅𝑻 + 𝒏𝑹𝒅𝑻
∴ 𝑪 𝒑 = 𝑪 𝑽 + 𝑹 The molar heat capacities and of an ideal gas differ by R , the ideal-gas consant . The dimensionless ratio of heat capacities , is denoted by .  

7. THE RATIO OF HEAT CAPACITY MONATOMIC GASES = 1.67   DIATOMIC GASES = 1.40  

8. EXAMPLE 1 A typical dorm room or bedroom contains about 2500 moles of air. Find the change in the internal energy of this much air when it is cooled from 35.0°C to 26.0°C at a constant pressure of 1.00 atm. Treat the air as an ideal gas with g = 1.400.

9. EXAMPLE 2 Three moles of an ideal monatomic gas expands at a constant pressure of 2.50 atm , the volume of the gas changes from to . Calculate the initial and find temperatures of the gas. (b)Calculate the amount of work the gas does in expanding. (c)Calculate the amount of heat added to the gas. (d)Calculate the change in internal energy of the gas.