Question

An insulated rigid vessel contains a mixture of fuel and air. The mixture is ignited by a minute spark. The contents of vessel experience
1. increase in temperature, pressure and energy
2. decrease in temperature, pressure and energy
3. increase in temperature and pressure but increase in energy
4. Increase in temperature and pressure but no change in energy

Answer 1

Correct Answer - Option 4 : Increase in temperature and pressure but no change in energy

Explanation:

According to the First Laws of Thermodynamics, the total energy remains constant.

The mathematical expressions of First Laws of Thermodynamics:

δQ = dU + δW.

Since the vessel is insulated no heat is going out and since the boundary is rigid no work is done by the system.

When the mixture is ignited by a minute spark there is a sudden rise in temperature.

Also from the perfect gas equation 

PV = mRT

where P = absolute pressure, V = volume, m = mass, R = gas constant, T = absolute temperature.

Here V (volume) remains constant, m and R are also constant for a gas.

So P ∝ T

i.e with the increase in temperature, pressure also gets increases.