Question

1.0 mole of gas is compressed from a pressure of 101.3 kPa to a pressure of 202.6 kPa without exchanging heat with the surroundings. The work required is 1573 kJ. What is the internal energy change?

A) 1573 kJ
B) 0 kJ
C) -1573 kJ
D) Cannot be determined

Answer 1

The change in internal energy of the gas in an adiabatic compression where 1573 kJ of work is done on the gas is -1573 kJ, as the first law of thermodynamics states ΔU = Q - W and Q is zero for adiabatic processes.

Step-by-step explanation:

The question is about the change in internal energy of a gas when it is compressed adiabatically, meaning without heat exchange with the surroundings. According to the first law of thermodynamics, the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). In mathematical terms, ΔU = Q - W. For an adiabatic process, Q is zero since there is no heat exchange, so the change in internal energy is simply ΔU = -W, where W is the work done on the gas.

Since 1573 kJ of work is done on the gas, the internal energy change is -1573 kJ which corresponds to option C). The negative sign indicates that the work is done on the system, thus increasing its internal energy.