Question

An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ______.

Options

• 42

• 46

• 45

• 41

Answer 1

An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is 46.

Explanation:

Given: Number of moles in a sample of diatomic ideal gas made up of rigid molecules is n = 5, temperature of gas is Ti = 20°C pressure of gas is P = 1 atm, the gas goes through an adiabatic compression, V_f = `"V"_"i"/10` the change in internal energy of the gas during the adiabatic process is ΔU = X kJ.

To find: The value of X.

For an adiabatic process:

`"T"_"i""V"_"i"^(gamma-1) = "T"_"f""V"_"f"^(gamma-1)`

`"T"_"f" = "T"_"i" ("V"_"i"/"V"_"f")^(gamma-1)`

γ = `7/5` for diatomic gas with rigid molecules.

Tf = (20 + 273) ×(10)^7/5-1

= 736 K

 ΔU = `1/2"fnR"("T"_"f"-"T"_"i") = 1/2xx5xx5xx8.31xx443`

 ΔU = 46016 J

 ΔU = 46 KJ

But ΔU = X KJ

So, X = 46