Numerical

**Solve the following.**

The volume of a given mass of a gas at 0°C is 2 dm^{3}. Calculate the new volume of the gas at constant pressure when the temperature is decreased by 10°C.

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#### Solution

**Given:**

T_{1} = Initial temperature = 0°C = 0 + 273.15 = 273.15 K,

V_{1} = Initial volume = 2 dm^{3}

T_{2} = Final temperature = 273.15 K − 10 = 263.15 K

**To find: **V_{2} = Final volume

**Formula:** `"V"_1/"T"_1="V"_2/"T"_2` (at constant n and P)

**Calculation:**

According to Charles’ law,

`"V"_1/"T"_1="V"_2/"T"_2` (at constant n and P)

∴ V_{2} = `("V"_1"T"_2)/"T"_1=(2xx263.15)/273.15` = 1.927 dm^{3}

The new volume of a given mass of gas is **1.927 dm ^{3}**

Concept: The Gas Laws

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