Find the total change in the internal energy of a gas that i

Find the total change in the internal energy of a gas that is subjected to the following two-step process. In the first step the gas is made to go through isochoric heating until 5560 J of heat is transferred into the gas and its pressure is 4.12 105 Pa. In the second step it is subjected to isobaric compression until its volume decreases by 7.70 103 m3 and 1240 J of heat is transferred out of the gas. What is the total change in internal energy of this gas?

Solution

In Isochoric process:

Heat is transferred into the gas Q = 5560 J

Heat is absorbed.So, we take Q is positive.

Work done in isochoric process W = 0

Since there is no change in volume in isochoric process

So, change in internal energy of the gas U = Q - W
                                                              = 5560 J

Isobaric compression :

Pressure P = 4.12 x10 5 Pa

Change in volume dV = -7.7 x10 ^-3 m ³

Here negative sign indicates the volume is decreases.

Work done W \' = P dV

                      = (4.12x10 ⁵)(-7.7x10 ^-3)

                      = -3172.4 J

heat is transferred out of the gas Q \' = - 1240 J

Here negative sign indicates that heat is emitted from the gas

Chang ein internal energy in this process U \' = Q \' - W\'

                                                                 = -1240 - (-3172.4)

                                                                 = 1932.4 J

Therefore the total change in internal energy of this gas = U + U \'

                                                                                = 5560 J +1932.4 J

                                                                                = 7492.4 J