Thermodynamics
Thermodynamics
- One mole of an ideal gas expands isothermally at 300 K to twice its initial volume. The work done by the gas is approximately (R = 8.314 J mol-1 K-1, ln 2 = 0.693) Answer: B. 1729 J W=nRTlnV₂/V₁=8.314×300×0.693≈1729 J. 1
- A Carnot engine has efficiency 40% with its sink at 300 K. Keeping the sink temperature constant, by how much should the source temperature be increased to raise the efficiency to 50%? Answer: C. 100 K 0.4=1-300/T₁⇒ T₁=500 K. For 50%: T₁'=600 K. Increase =100 K. 1
- A hypothetical thermodynamic cycle is shown in the figure. Calculate the work done in 25 cycles. Given : a = fracΔV_max2=6-2/2×10⁻³m³ = 2 x 10⁻³ m³, b = fracΔP_max2=11-1/2×10⁵Pa = 5 x 10^(5 )Pa Cycles = 25 The work done in one cycle, oin... 1
- An ideal monatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. Given : T_f = 2T_i, monatomic gas ϒ = 5/3 P_iV_i^ϒ = P_fV_f^ϒ in an adiabatic process Now, PV= nRT ∴ V = nRT/P ∴ V_(i )= nRT_i/P_i and V_(f... 1
- An ideal gas is taken through an isothermal process. If it does 2000 J of work on its environment Given : W = 2000J , isothermal process In this case, the change in the internal energy of the gas, ΔU=0, as the gas is taken through an isot... 1
- A Carnot refrigerator operates between 250ºK and 300ºK. Calculate its coefficient of performance. Given : T_C = 250 K, T_H = 300 K K = T_C/T_H-T_C=250/300-250=250/50 = 5 this is the coefficient of performance of the refrigerator. 1
- Efficiency of a Carnot cycle is 75%. If temperature of the hot reservoir is 727ºC Given : η = 75% = 0.75, T_H = (273 + 727) K = 1000 K η = 1−T_C/T_H ∴ T_C/T_H= 1− η T_C = T_H (1 − η ) = 1000(1 - 0.75) = 250 K = (250 − 273)... 1
- A system releases 125 kJ of heat while 104 kJ of work is done on the system. Calculate the change in internal energy. Given: Q = −125kJ, W= −104kJ ΔU = Q − W= −125−(−104) = (−125 + 104) = −21kJ. Negative sign shows that decrease in energy. This is the change... 1
- A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm Data: P = 1 atm = 1.013 x 10⁵ Pa, V₁ =5 litres =5 x 10⁻³ m³, V₂ = 10 Litres = 10 x 10⁻³ m³, Q = 400J. The work done by the system (gas in th... 1
- A mixture of hydrogen and oxygen is enclosed in a rigid insulting cylinder. It is ignited by a spark. The internal energy of a system is the sum of potential energy and kinetic energy of all the constituents of the system. In the example stat... 2
- Why should a Carnot cycle have two isothermal two adiabatic processes? With two isothermal and two adiabatic processes all reversible, the efficiency of the Carnot engine depends only on the temperatures of the... 1
- What sets the limits on efficiency of a heat engine? The temperature of the cold reservoir sets the limit on the efficiency of a heat engine. [Note: η = 1-T_C/T_H This formula shows that for ma... 1
- Give an example of some familiar process in which heat is added to an object, without changing its temperature. (a) Melting of ice (b) Boiling of water 2
- Give an example of some familiar process in which no heat is added to or removed form a system Answer: Any adiabatic process, for example the sudden bursting of a cycle tyre (air cools) or quickly compressing air in a bicycle pump (air... 1
- A gas contained in a cylinder surrounded by a thick layer of insulating material is quickly compressed. If a gas contained in a cylinder surrounded by a thick layer of insulating material is quickly compressed then (a) There is no transfer of h... 1
- During refrigeration cycle, heat is rejected by the refrigerant in the (A) condenser 2
- The second law of thermodynamics deals with transfer of: (A) work done (B) energy (C) momentum (D) heat Answer: (D) heat The second law of thermodynamics tells us the direction in which heat flows and how much of it can be converted into work:... 1
- Efficiency of a Carnot engine is large when (A) TH is large (A) T_H is large (B) T_C is low (C) T_H – T_C is large [ η = T_H-T_C/T_H=1-T_C/T_H , ] 1
- Which of the following is an example of the first law of thermodynamics? Answer: (D) After falling down the hill, a ball's kinetic energy plus heat energy equals the initial potential energy. The first law of ther... 1
- A gas in a closed container is heated with 10J of energy, causing the lid of the container to rise 2m with 3N of force (B) 4J the total change in energy of the system is 4J 2