| A piston moves upwards by 5 cm, when 200 J of heat is added. |
 |
| Spring has a spring constant of \[50kN{{m}^{-1}}\]and is initially unstretched. Mass of piston is 60 kg and its diameter is 20 cm. Change of internal energy of vapour is |
A) 200 J
B) 280 J
C) 50 J
D) \[-\,50\,J\]
Correct Answer: D
Solution :
| Work needed to raise the piston and compress the spring is. \[W=mgh+\frac{1}{2}k{{x}^{2}}+{{p}_{\text{atm}}}A\cdot h\] |
| \[=60\times 9.8\times 0.05+\frac{1}{2}\times 50000\times {{(0.05)}^{2}}\]\[+\frac{100000\times \pi \times {{(0.2)}^{2}}}{4}\times 0.05\] |
| \[=250J\] |
| By first law of thermodynamics, we have |
| \[\Delta U=\Delta Q-\Delta W=200-250=-50J\] |
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