When a gas filled in a closed vessel is heated by raising the temperature by 1°C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

Solution

Physics sir · 4 steps

Closed vessel means fixed volume, so the fractional rise in pressure equals that in temperature.

1. Fixed volume. The vessel is closed and rigid, so V and the amount of gas stay the same. From PV = nRT, this gives P ∝ T, with T in kelvin.

   (Δ P)/P = (Δ T)/T

2. Put in numbers. A rise of 1 °C is the same as a rise of 1 K, so Δ T = 1 K. A 0.4% rise in pressure means (Δ P)/P = 0.4/100 = 0.004.
3. Solve for T. 0.004 = 1/T, so T = 1/0.004 = 250 K.
4. So. The initial temperature of the gas is 250 K.

The common slip: 25. Reading 0.4% as 0.04 instead of 0.004 gives 25 K, not 250. Divide the percentage by 100 to get the fraction.

The idea to keep. At constant volume, P ∝ T, so a small percentage change in pressure equals the same percentage change in absolute temperature. A change of 1 °C is always a change of 1 K.

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