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 Carnot engine has an efficiency of 50% when its source is at a temperature 327^° C. The temperature of the sink is : Answer: 2. 27^° C Carnot efficiency: η=1-T₂/T₁ with temperatures in kelvin. T₁=327+273=600 K, η=0.5⇒ T₂=0.5×600=300 K = 27^° C. The answer i... 1
- An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is : Answer: 3. 2 On a P-V diagram, all processes start from the same point. Curve 1 is vertical (constant volume, isochoric) and curve 4 is hori... 1
- Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened.… Answer: 2. adiabatic The system is thermally insulated, so no heat enters or leaves: Q=0 . That makes the process adiabatic. (This is a free... 1
- In which of the following processes, heat is neither absorbed nor released by a system ? Answer: 2. adiabatic In an adiabatic process Δ Q=0 by definition: no heat enters or leaves the system. In isothermal, isobaric and isochoric... 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
- A carnot engine having an efficiency of 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is : Answer: 1. 90 J Key idea: as a refrigerator, coefficient of performance =Q₂/W=1-η/η . η=tfrac110⇒Q₂/W=9/10/1/10=9 . Q₂=9×10=90 J absorbed fr... 1
- The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is Answer: 1. 26.8% Efficiency of an ideal (Carnot) engine is η=1-T₂/T₁ , with temperatures in kelvin. T₂=273 K (freezing point), T₁=373 K (boi... 1
- Thermodynamic processes are indicated in the following diagram.Match the following :Column-1: P. Process I; Q. Process II; R. Process III; S. Process IVColumn-2: a. Adiabatic; b. Isobaric; c. Isochoric; d. Isothermal Answer: 1. P → c, Q → a, R → d, S → b Key idea: identify each process from the P-V diagram. I: vertical line, volume constant, isochoric (c)... 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
- The temperature inside a refrigerator is t_2°C and the room temperature is t_1°C. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be Answer: 1. t₁+273/t₁-t₂ The refrigerator works as a heat pump. Ideally its coefficient of performance for the heat delivered to the room is... 1
- A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then : Answer: 2. Compressing the gas through adiabatic process will require more work to be done. Key idea: compare areas under the P-V curves. Fo... 1
- A refrigerator works between 4^° C and 30^° C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is : (Take 1 cal = 4.2 Joules) Answer: 3. 236.5 W Key idea: for a refrigerator, COP=T₂/T₁-T₂=Q₂/W . T₂=277 K, T₁=303 K, so COP =277/26≈10.65 . Heat removed per second =600... 1