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11.Thermodynamics
normal
Two cylinders of equal size are filled with equal amount of ideal diatomic gas at room temperature. Both the cylinders are fitted with pistons. In cylinder A the piston is free to move while in $B$ position is fixed. When same amount of heat is supplied to both the cylinders, the temperature of the gas cylinder $A$ raises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B.$
A
$42\;K$
B
$30\;K$
C
$20\;K$
D
$56\;K$
Solution
Cylinder $A$ and $B$ undergoes isobaric and isochoric process.
$Q _{ A }= n C _{ p } \Delta T$
$Q _{ B }= n C _{1} \Delta T$
$\because Q _{ A }= Q _{ B }$
$nC _{ v } \Delta T = nC _{ p } \Delta T$
$\Delta T =\frac{ C _{ p }}{ C _{ v }} \Delta T$
$\Delta T =\frac{7}{5} \times 30=42\; K$
Standard 11
Physics
