An ideal gas does work on its surroundings when it expands by $$2.5\,L$$  against external pressure $$2\,atm.$$  This work done is used to heat up $$1\,mole$$  of water at $$293\,K.$$  What would be the final temperature of water in Kelvin if specific heat for water is $$4.184\,J\,{g^{ - 1}}{K^{ - 1}}?$$

Solution :
Work done,
$$\eqalign{ & w = - {P_{ext.}}\,\,dV \cr & w = - 2 \times 2.5 \cr & \,\,\,\,\,\, = - \,5\,L\,atm \cr & \,\,\,\,\,\, = - 506.3\,J \cr} $$
Because this work is used in raising the temperature of water, so work done is equal to the heat supplied i.e.,
$$w = q = m \cdot {c_s} \cdot \Delta T$$
Given that, $$m = 18\,g\left( { = 1\,mole} \right),{c_s} = 4.184\,J\,{g^{ - 1}}\,{K^{ - 1}},$$         $$q = + 506.3\,J\,$$   ( Heat is given to water ), $$\Delta T = ?$$
$$\eqalign{ & \Delta T = \frac{q}{{{c_s} \cdot m}} \cr & \,\,\,\,\,\,\,\,\, = \frac{{506.3}}{{4.184 \times 18}} \cr & \,\,\,\,\,\,\,\,\, = 6.72 \cr} $$
∴ Final temperature,
$$\eqalign{ & {T_f} = {T_i} + \Delta T \cr & \,\,\,\,\,\,\,\, = 293 + 6.72 \cr & \,\,\,\,\,\,\,\, = 299.72\,K \approx 300\,K \cr} $$