a. You need to raise the temperature of a gas by 10 degrees Celsius. To use the

Question

a. You need to raise the temperature of a gas by 10 degrees Celsius. To use the least amount of heat energy how should you heat the gas at constant pressure or constant volume? Explain.

b. A gas is compressed from 800cm^3 to 200cm^3 at a constant pressure of 400kPa. At the same time, 100 J of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?

c. What work would have been done on this gas if the compression has been isothermal from the same starting conditions?

Explanation / Answer

(a). least amount of heat required in constant volume process. Since at constant volume the total heat is used to increase the internal energy only. at constant pressure the total heat is used to increase the internal energy as well as external work. Note : - if internal energy is increases then temperature is increases. (b). pressure P = 400*10^3 Pa Initial volume V = 800 cm^ 3 = 800 * 10 ^-6 m^ 3 final volume V ' = 200 cm^ 3 = 200* 10 ^-6 m^ 3 work done W = P ( V ' - V )                         = -240 J heat transferred Q = -100 J Change in internal energy U = Q -W                                            = 140 J (c). work done in isothermal process   W = nRT ln( V ' / V ) where T = temperature = PV / nR So, W = PV ln( V ' / V )     Since PV = nRT            = 320 ln( 200 /800)            = -443.61 J

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