An ideal gas in a rigid container (constant volume) has its pressure cut in half slowly. In the process, 265 kJ of heat left the gas. (a) How much work was done during the process? (b) What was the change in internal energy of the gas during this process?

No Cheating

To find the answers to these questions, we can make use of the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

(a) To find the work done during the process, we need to calculate the amount of work done when the pressure of the gas is cut in half.

Work can be represented using the equation:
Work = Pressure * Change in Volume

In this case, the volume remains constant, so the change in volume is zero. Therefore, the work done during this process is zero.

(b) To find the change in internal energy of the gas, we can use the equation:
Change in Internal Energy = Heat added - Work done

In this case, we have the value of heat that left the gas, which is -265 kJ (negative sign indicates that heat is leaving the gas). And we just found out that the work done is zero.

Therefore, the change in internal energy of the gas during this process is:
Change in Internal Energy = -265 kJ - 0
Change in Internal Energy = -265 kJ

So, the change in internal energy of the gas during this process is -265 kJ.