Question

When a certain amount of a gas is heated, its volume in-
creases by 40% and pressure decreases by 20%. If initial
temperature is 16°C, calculate final temperature of the gas.​

Answer 1

Answer:

$final \: \: temperature \: \: of \: \: the \: \: gas \\ = > 323.68 \: K$

Explanation:

$If \: \: initial \: \: pressure \: \: is \: \: P \: \\ Final \: \: pressure \: \: is \: \\ = > P \: - \frac{20}{100} of \: P \: = 0.8 \: P$

$If \: \: initial \: \: volume \: \: is \: \: V \\ Final \: \: volume \: \: is \\ = > V + \frac{40}{100} of \: V = 1.4 \: V$

$If \: \: initial \: \: temperature \: \: is \: \: 16 {}^{o} C \\ = > 16 + 273 = 289 \: K \\ Then \: \: final \: \: temperature = ? \: K$

$According \: \: to \: \: the \: \: gas \: \: equation \\ \frac{P _{1} V _{1} }{T _{1}} = \frac{P _{2} V _{2} }{T _{2}}$

$= > \frac{P \: \times \: V}{289} = \frac{0.8 \: P \: \times \: 1.4 \: V}{T_{2}}$

$= > T_{2} = 0.8 \times 1.4 \times 289 \\ = 323.68 \: K$

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