
One litre of helium gas at a pressure of 76 cm-hg and temperature is heated till its pressure and volume are doubled. The final temperature attained by the gas is
(A)
(B)
(C)
(D)
Answer
478.2k+ views
Hint: We need to assume that the gas is ideal. Compare the first state to the second state and make the temperature of the second state subject of the formula
Formula used: In this solution we will be using the following formulae;
where is the pressure at the first state, is the volume at the first state, and is the temperature at the first state. Similarly, is the pressure at the second state, is the volume at the second state, and is the temperature at that state.
Complete step by step solution:
To solve the above question, we assume that the helium gas is behaving like an ideal gas. Hence, we can use the ideal gas relation. From the ideal gas relation, we can get by comparison of the two state, the equation
where is the pressure at the first state, is the volume at the first state, is the temperature at the first state, is the pressure at the second state, is the volume at the second state, and is the temperature at that state.
Hence, by inserting all given values, we have
( since temperature has to be in kelvin)
Hence,
Which by computation gives
Which by conversion to degree Celsius is
Hence, the correct answer is B.
Note:
Alternatively, observe that we do not need to insert the values for pressure and volume since we were told that it was doubled. We could simply write the equation as
Hence, the pressure and volume values cancel out. So we have
From which we get
.
Formula used: In this solution we will be using the following formulae;
Complete step by step solution:
To solve the above question, we assume that the helium gas is behaving like an ideal gas. Hence, we can use the ideal gas relation. From the ideal gas relation, we can get by comparison of the two state, the equation
Hence, by inserting all given values, we have
Hence,
Which by computation gives
Which by conversion to degree Celsius is
Hence, the correct answer is B.
Note:
Alternatively, observe that we do not need to insert the values for pressure and volume since we were told that it was doubled. We could simply write the equation as
Hence, the pressure and volume values cancel out. So we have
From which we get
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