Use (V P)/(T)=(V^' P^')/(T^') to find each quantity. (All...

Use $\frac{V P}{T}=\frac{V^{\prime} P^{\prime}}{T^{\prime}}$ to find each quantity. (All pressures are absolute unless otherwise stated.) $V=532 \mathrm{~m}^{3}, P=135 \mathrm{kPa}, T=87^{\circ} \mathrm{C}, V^{\prime}=379 \mathrm{~m}^{3}, P^{\prime}=123 \mathrm{kPa} ;$ find $T^{\prime}$.

Use $\frac{V P}{T}=\frac{V^{\prime} P^{\prime}}{T^{\prime}}$ to find each quantity. (All pressures are absolute unless otherwise stated.)
$V=532 \mathrm{~m}^{3}, P=135 \mathrm{kPa}, T=87^{\circ} \mathrm{C}, V^{\prime}=379 \mathrm{~m}^{3}, P^{\prime}=123 \mathrm{kPa} ;$ find $T^{\prime}$.

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Key Concepts

Combined Gas Law

The combined gas law expresses the relationship between pressure, volume, and temperature for a given amount of gas. It states that the ratio of the product of pressure and volume to temperature remains constant during a change of state. This law is fundamental when solving problems where several state variables change simultaneously.

Absolute Temperature

Gas law calculations must be performed using the absolute temperature scale, measured in Kelvin, because the relationships between pressure, volume, and temperature are derived under conditions where temperature is taken from absolute zero. Converting from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.

Algebraic Manipulation

Solving gas law problems, such as finding an unknown state variable, involves algebraic manipulation to rearrange equations. This includes isolating the desired variable and substituting the known values correctly, ensuring consistency in units throughout the calculation.

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