Adiabatic Heating of Air and Increase in Internal Energy

Introduction
When a gas is heated without receiving or losing any heat to the surroundings, it is called an adiabatic process. In this case, the gas undergoes a change in internal energy as the temperature and pressure of the gas increase.

Adiabatic Heating of Air
When 1 kg of air is heated adiabatically from 0°C to 10°C, the temperature of the air increases by 10°C. The pressure of the air also increases due to the increase in temperature. The specific heat ratio (γ) for air is 1.4, which means that the ratio of specific heats for air at constant pressure and constant volume is 1.4.

Increase in Internal Energy
The increase in internal energy of the air can be calculated using the following formula:

ΔU = (γ / (γ - 1)) x m x R x ΔT

where ΔU is the change in internal energy, m is the mass of the air (1 kg in this case), R is the gas constant for air (287 J/kgK), γ is the specific heat ratio for air (1.4), and ΔT is the change in temperature (10°C in this case).

Substituting the values in the formula, we get:

ΔU = (1.4 / (1.4 - 1)) x 1 x 287 x 10
ΔU = 4018.57 J

Therefore, the increase in internal energy of the air is 4018.57 J.

Conclusion
In conclusion, when 1 kg of air is heated adiabatically from 0°C to 10°C, the temperature and pressure of the air increase, and the internal energy of the air increases by 4018.57 J.

PV=NRT

N=RT\V
N=831.4×0/1.4
=593.85gk