NEET · Physics · STD 11 - 11. thermodynamics
Two gases \(A\) and \(B\) are filled at the same pressure in separate cylinders with movable pistons of radius \(r_A\) and \(r_B\), respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas \(A\) and \(B\) are displaced by 16 cm and 9 cm , respectively. If the change in their internal energy is the same, then the ratio \(\frac{r_A}{r_B}\) is equal to
- A \(\frac{4}{3}\)
- B \(\frac{3}{4}\)
- C \(\frac{2}{\sqrt{3}}\)
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
According to question
Pressure is constant \(P_A=P_B\)
\(Q _{ A }= Q _{ B }\)
\(\Delta U _{ A }= U _{ B }\)
So according to I law
\(Q =\Delta U + w \)
\( w _1= W _2 \)
\( P _1 \Delta V_1= P _2 \Delta V_2 \)
\( \left(\pi r _{ A }^2\right) x _{ B }=\left(\pi r _{ B }^2\right) x _{ A } \)
\( \frac{ r _{ A }}{ r _{ B }}=\sqrt{\frac{ x _{ B }}{ x _{ A }}}=\sqrt{\frac{9}{16}}=\frac{3}{4}\)
Pressure is constant \(P_A=P_B\)
\(Q _{ A }= Q _{ B }\)
\(\Delta U _{ A }= U _{ B }\)
So according to I law
\(Q =\Delta U + w \)
\( w _1= W _2 \)
\( P _1 \Delta V_1= P _2 \Delta V_2 \)
\( \left(\pi r _{ A }^2\right) x _{ B }=\left(\pi r _{ B }^2\right) x _{ A } \)
\( \frac{ r _{ A }}{ r _{ B }}=\sqrt{\frac{ x _{ B }}{ x _{ A }}}=\sqrt{\frac{9}{16}}=\frac{3}{4}\)
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