0.08 kg air is heated at constant volume through 5° C. The specific heat of air at constant volume is 0.17 kcal / kg° C and J=4.18 joule/ cal. The change in its internal energy is approximately.

Solution

Physics sir · 4 steps

Constant volume means no work is done, so every joule of heat goes into internal energy.

1. No work done. At constant volume the gas does not expand, so W = 0. The first law Q = Δ U + W then gives Δ U = Q.

   Δ U = m cᵥ Δ T

2. Heat in calories. Q = 0.08 × 0.17 × 5 = 0.068 kcal = 68 cal.
3. Convert to joules. Multiply by J = 4.18 J/cal: 68 × 4.18 = 284.24 J.
4. So. Δ U ≈ 284 J, which is option (c).

The idea to keep. At constant volume, W = 0 and Δ U = m cᵥ Δ T. If cᵥ is in kcal, convert kcal to cal first, then multiply by J to get joules.

Answer from the NTA final answer key. Solution by PrepWiser.