Question

v1 = 84 cu/ft
p1 = 300 psi
t1 = 48°c

v2 =????? cu/ft
p2 = 110 psi
t2 = 30°c

Explanation:

Step1: Convert temperatures to Kelvin

To use the ideal gas law (combined gas law), temperatures must be in Kelvin. The formula to convert Celsius to Kelvin is \( T(K) = T(^\circ C) + 273.15 \).
For \( T_1 \): \( T_1 = 48 + 273.15 = 321.15 \, K \)
For \( T_2 \): \( T_2 = 30 + 273.15 = 303.15 \, K \)

Step2: Apply the combined gas law

The combined gas law is \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \). We solve for \( V_2 \):
\( V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} \)

Substitute the values:
\( V_1 = 84 \, \text{cu/ft} \), \( P_1 = 300 \, \text{psi} \), \( P_2 = 110 \, \text{psi} \), \( T_1 = 321.15 \, K \), \( T_2 = 303.15 \, K \)

\( V_2 = 84 \times \frac{300}{110} \times \frac{303.15}{321.15} \)

Step3: Calculate the fractions

First, \( \frac{300}{110} \approx 2.7273 \)
Second, \( \frac{303.15}{321.15} \approx 0.9439 \)

Multiply these with \( V_1 \):
\( V_2 \approx 84 \times 2.7273 \times 0.9439 \)

Step4: Final calculation

\( 84 \times 2.7273 \approx 229.0932 \)
\( 229.0932 \times 0.9439 \approx 216.2 \)

Answer:

\( V_2 \approx 216.2 \, \text{cu/ft} \)