Applying the First Law

An ideal gas is heated at 2.0 × 10⁵ Pa. Its volume increases from 0.038 m³ to 0.063 m³, and its internal energy increases by 7600 J. Find the thermal energy supplied (9702/41/O/N/23 Q2(b)).

1. Find the increase in volume.
   $$\Delta V=0.063-0.038$$
   $$\Delta V=0.025\ \mathrm{m^3}$$
2. The gas expands, so work done on it is negative.
   $$W_{\mathrm{on}}=-p\Delta V$$
   $$p\Delta V=(2.0\times10^5)(0.025)$$
   $$W_{\mathrm{on}}=-5000\ \mathrm{J}$$
3. Substitute the increase in internal energy and the signed work.
   $$7600=q-5000$$
4. $$q=12600\ \mathrm{J}$$

A substance vaporises at pressure 1.0 × 10⁵ Pa. Its volume increases by 0.017 m³ and its internal energy increases by 17.6 kJ. Find the thermal energy supplied (9702/42/O/N/24 Q3(b)).

1. First find the magnitude of the work done by the substance.
   $$W_{\mathrm{by}}=p\Delta V$$
   $$W_{\mathrm{by}}=(1.0\times10^5)(0.017)$$
   $$W_{\mathrm{by}}=1.7\ \mathrm{kJ}$$
2. Expansion means work done on the substance is negative.
   $$W=-1.7\ \mathrm{kJ}$$
3. $$17.6=q-1.7$$
   $$q=19.3\ \mathrm{kJ}$$