Question

In a 39.0 L expansion unit of a heat pump, the gas is at 4 ∘C and 415 kPa . The gas is compressed to 6.5 L . What must the pressure be in the compressor to achieve 48 ∘C ?

Answer 1

To solve this problem, we can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume when the temperature is constant.

Boyle's Law equation:

P1 * V1 = P2 * V2

Where:

P1 = Initial pressure

V1 = Initial volume

P2 = Final pressure (what we need to find)

V2 = Final volume

Given information:

Initial volume (V1) = 39.0 L

Initial pressure (P1) = 415 kPa

Final volume (V2) = 6.5 L

Final temperature (T2) = 48 °C

First, we need to convert the temperature from Celsius to Kelvin:

T2 = 48 °C + 273.15 = 321.15 K

Now, we can plug in the values into Boyle's Law equation and solve for P2:

P1 * V1 = P2 * V2

415 kPa * 39.0 L = P2 * 6.5 L

Solving for P2:

P2 = (415 kPa * 39.0 L) / 6.5 L

P2 ≈ 2490 kPa

Therefore, the pressure in the compressor must be approximately 2490 kPa to achieve a temperature of 48 °C in a compressed volume of 6.5 L.