Question

The following question appears on a quiz: "You fill a tank with gas at 60°C to 100 kPa and seal it. You decrease the temperature to 10°C but keep the volume constant. What happens to the pressure?" A student answers that the new pressure will be 17 kPa. Which of the following explanations is true?

The student did not solve for the correct parameter, and the answer should be 50 kPa.

The student did not solve for the correct parameter, and the answer should be 600 kPa.

The student did not work with absolute temperatures, and the answer should be 85 kPa.

The student did not work with absolute temperatures, and the answer should be 888 kPa.

Answer 1

The student did not work with absolute temperatures, and the answer should be 85 kPa.

Step-by-step explanation:

We can use the general law of ideal gas: PV = nRT.

where, P is the pressure of the gas in atm.

V is the volume of the gas in L.

n is the no. of moles of the gas in mol.

R is the general gas constant,

T is the temperature of the gas in K.

If n and V are constant, and have two different values of P and T:

P₁T₂ = P₂T₁

P₁ = 100.0 kPa, T₁ = 60.0°C + 273 = 333.0 K.

P₂ = ??? kPa, T₂ = 10.0°C + 273 = 283.0 K.

∴ P₂ = P₁T₂/T₁ = (100.0 kPa)(283.0 K)/(333.0 K) = 84.98 kPa ≅ 85.0 kPa.

So, the right choice is:

The student did not work with absolute temperatures, and the answer should be 85 kPa.

Answer 2

The student did not work with absolute temperatures, and the answer should be 85 kPa.

Step-by-step explanation:

• We can use the general law of ideal gas: PV = nRT.

where, P is the pressure of the gas in atm.

V is the volume of the gas in L.

n is the no. of moles of the gas in mol.

R is the general gas constant,

T is the temperature of the gas in K.

• If n and V are constant, and have two different values of P and T:

P₁T₂ = P₂T₁

P₁ = 100.0 kPa, T₁ = 60.0°C + 273 = 333.0 K.

P₂ = ??? kPa, T₂ = 10.0°C + 273 = 283.0 K.

∴ P₂ = P₁T₂/T₁ = (100.0 kPa)(283.0 K)/(333.0 K) = 84.98 kPa ≅ 85.0 kPa.

• So, the right choice is:

The student did not work with absolute temperatures, and the answer should be 85 kPa.