First law of 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… Answer: 2. 3/4 Key idea: at constant pressure, Q=Δ U+W with W=pΔ V . The heat supplied and Δ U are the same for both gases, so W is equal. W... 1
- A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is : Answer: 2. zero Key idea: Work done by a gas is W=∫ P dV , so it is zero when the volume does not change. In the figure, path bc is vertical... 1
- A sample of 0.1 g of water at 100°C and normal pressure (1.013×10^5 Nm^-2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is Answer: 3. 208.7 J First law: Δ U=Q-W , with W=PΔ V . Q=54×4.18≈225.7 J. Volume change: steam 167.1 cc minus water 0.1 cc, Δ V=167\ cm³=1.67... 1
- The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is Answer: 1. 2/5 The graph is a straight line through the origin, so V∝ T : the process is at constant pressure. For a monatomic gas, W=nRΔ T... 1
- One mole of an ideal monatomic gas undergoes a process described by the equation PV^3 = constant. The heat capacity of the gas during this process is Answer: 3. R For a polytropic process PV^x= const, molar heat capacity is C=C_v+R/1-x . Monatomic gas: C_v=3/2R ; here x=3 . C=3/2R+R/1-3=3/... 1