The Combined Gas Law . In an autoclave, steam at 100°C is generated at 1.00 atm. After the autoclave is closed, the steam is heated at constant volume until the pressure gauge indicates 1.13 atm. What is the final temperature in the autoclave?

Question

Strategy : All temperatures in gas law calculations must be in kelvins; therefore, we must first convert the Celsius temperature to kelvins. Then we identify the known quantities. Because [latex]V_{1} and V_{2} [/latex] are the same in this example and consequently cancel each other, we don’t need to know the volume of the autoclave.

Accepted Answer

Step 1: Convert from degrees C to degrees K.

100°C = 100 + 273 = 373 K

Step 2: Identify the known quantities.

Initial: [latex] P_{1} = 1.00 atm [/latex] [latex]T_{1} = 373 K [/latex]

Final: [latex]P_{2} = 1.13 atm [/latex] [latex]T_{2} = ? [/latex]

Step 3: Solve the combined gas law equation for [latex] T_{2} [/latex] , the new temperature.

[latex]T_{2} =\frac{P_{2} \cancel{V_{2} }T_{1} }{P_{1} \cancel{V_{1}}}=\frac{ (1.13 \cancel{atm}) (373 K )}{1.00 \cancel{atm}} = 421 K [/latex]

The final temperature is 421K, or 421 - 273 = 148°C.

Question 5.2: The Combined Gas Law . In an autoclave, steam at 100°C is ge...

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