Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is 22 ℃. During the day, the temperature…

Question

Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is 22 ℃. During the day, the temperature rises to 42 ℃ and the tube expands by 2%. The pressure of the air in the tube at this temperature will be approximately

MARKS Content Team · Accepted Answer

Correct answer: (B) 209 kPa. The ideal gas law is the equation of state of an ideal gas. The state of an amount of gas is determined by its pressure, volume and temperature. The equation has the form pV=nRT where, p is pressure, V the volume, n the number of moles, R the gas constant and T the temperature. ∴ (p_1V_1T_1=p_2V_2T_2Given, p_1=200 kPa, V_1=V, T_1=273+22=295 K, V_2=V+0.02 VT_2=273+42=315 K200×V)/295=(p_2×1.02V)/315 ⇒ p_2=(200×315)/(295×1.02) p_2=209 kPa

Air is pumped into an automobile tube up to a pressure of $200 kPa$ in the morning when the air temperature is $22 ℃$ . During the day, the temperature rises to $42 ℃$ and the tube expands by $2 %$ . The pressure of the air in the tube at this temperature will be approximately

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