An ideal gas of n moles is taken from state 1 to state 2. On a pressure-temperature ( P-T ) diagram, this process is represented by a straight line passing through the origin. If the temperature of the gas changes from T₁ to T₂ , the work done by the gas is:

Step-by-step solution

According to the ideal gas equation, PV = nRT , which can be rearranged as P = ( nR V )T . The process is given as a straight line passing through the origin on the P-T diagram. The equation of such a line is P = kT , where k is a constant slope. Comparing the two equations, we get nR V = k . Since n , R , and k are constants, the volume V must also be constant. A process where the volume remains constant is an isochoric process ( V = 0 ). The work done by a gas is given by W = P , dV . Since there is no change in