Question

A 10 litre gas is inserted into a car tyre at 4 ATM and 27 degree Celsius the temperature of the tire increased 57 degrees celsius during driving what would be the pressure of gas during driving ​

Answer 1

GIVEN :

Volume of gas inserted into a car tyre (V) = 10 L

Initial pressure of the gas (P₁) = 4 atm

Initial temperature of the gas (T₁) = 27 °C

Increased temperature of the tyre (T₂) = 57 °C

TO FIND :

The pressure of the gas while driving.

SOLUTION :

• The temperature of the gas should be changed into its S.I. unit, Kelvin, as the volume and pressure are also in their respective S.I. units.

• We know that 1 °C = 273 K

∴  27 °C = (27 + 273) K = 300 K

• Given, increased temperature of the tyre (T₂) = 57 °C

Now, 57 °C = (57 + 273) K = 330 K

• Since the pressure of the gas filled in the same tyre is to be calculated, the volume of the gas remains unchanged.

• Applying the general gas equation, P₁V₁ / T₁ = P₂V₂ / T₂, we get;

P₁V / T₁ = P₂V / T₂ [ Since volume remains constant ]

=> P₁ / T₁ = P₂ / T₂ -(i)

• Substituting the necessary values in equation (i), we get;

4 atm / 300 K = P₂ / 330 K

=> P₂ = (4 atm × 330 K) / 300 K

=> P₂ = 4.4 atm

Answer - The pressure of the gas would be 4.4 atm while driving.