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Page 1 JEE Solved Example on Thermodynamics JEE Mains Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? ° ?? at ?? . ?? × ???? ?? ???????????? (A) ?? . ?? × ???? ???? (B) ?? × ???? ???? (C) ?? × ???? ???? (D) ?? . ?? × ???? ???? Ans: (A) ?? = 7 L = 7 × 10 -3 m 3 ?? = 273 K P = 1.3 × 10 5 Pa ? m = PV RT = 1.3 × 10 5 × 7 × 10 -3 8.314 × 273 ? 0.4 moles ? No. of molecules = 0.4 × 6.02 × 10 23 = 2.4 × 10 23 molecules Q2: An ideal gas mixture filled inside a balloon expands according to the relation ???? ?? /?? = constant. The temperature inside the balloon is (A) Increasing (B) Decreasing (C) Constant (D) Can't be said Ans: (A) PV 2/3 = const. ? nRT V V 2/3 = const. ? TV -1/3 = const. ? T = conts. × V 1/3 ? On increasing volume, temperature increase Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen supplied to the tank is: (A) ?? ???? (B) ???? ???? (C) ???? ???? (D) ???? ???? Ans: (C) T = constant, V = constant, Page 2 JEE Solved Example on Thermodynamics JEE Mains Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? ° ?? at ?? . ?? × ???? ?? ???????????? (A) ?? . ?? × ???? ???? (B) ?? × ???? ???? (C) ?? × ???? ???? (D) ?? . ?? × ???? ???? Ans: (A) ?? = 7 L = 7 × 10 -3 m 3 ?? = 273 K P = 1.3 × 10 5 Pa ? m = PV RT = 1.3 × 10 5 × 7 × 10 -3 8.314 × 273 ? 0.4 moles ? No. of molecules = 0.4 × 6.02 × 10 23 = 2.4 × 10 23 molecules Q2: An ideal gas mixture filled inside a balloon expands according to the relation ???? ?? /?? = constant. The temperature inside the balloon is (A) Increasing (B) Decreasing (C) Constant (D) Can't be said Ans: (A) PV 2/3 = const. ? nRT V V 2/3 = const. ? TV -1/3 = const. ? T = conts. × V 1/3 ? On increasing volume, temperature increase Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen supplied to the tank is: (A) ?? ???? (B) ???? ???? (C) ???? ???? (D) ???? ???? Ans: (C) T = constant, V = constant, ?? ?? = 35 28 = 1.25 Kmoles ? ?? ?? = ???? ?? = const. ? ?? ?? ?? ?? = ?? ?? ?? ?? ? ?? ?? = ?? ?? ?? ?? × ?? ?? = 9 6 × 35 28 ˜ 1.875 kmoles ? Moles of O 2 supplied = 1.875 - 1.25 = 0.625kmoles ? Amount of oxygen = 20 kg Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to maintained original pressure. The temperature ?? is equal to (A) ?????? ?? (B) ?????? ?? (C) ?????? ?? (D) ???? ?? Ans: (B) ???? = 4 ?? ???? ???? = ( 4 - 0.8) ?? ?? ( ?? + 50) = 3.2?? ?? ( ?? + 50) By (i) and (ii) we get, 4 ?? ???? = 3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50 ? ?? = 200 ?? Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ???? ° ?? the pressure is found to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5 atmosphere. The ratio of the molecular weights of these gases will be (A) ?? : ?? (B) 3:1 (C) ?? : ?? (D) ?? : ?? Ans: (A) For P = 1 atm , m 1 = 2gms , T = 298 K ? 1 × ?? = 2?? ?? 1 × 298 For ?? = 1.5 atm, ?? 1 = 2gm , ?? 2 = 3gm , ?? = 298 K. Page 3 JEE Solved Example on Thermodynamics JEE Mains Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? ° ?? at ?? . ?? × ???? ?? ???????????? (A) ?? . ?? × ???? ???? (B) ?? × ???? ???? (C) ?? × ???? ???? (D) ?? . ?? × ???? ???? Ans: (A) ?? = 7 L = 7 × 10 -3 m 3 ?? = 273 K P = 1.3 × 10 5 Pa ? m = PV RT = 1.3 × 10 5 × 7 × 10 -3 8.314 × 273 ? 0.4 moles ? No. of molecules = 0.4 × 6.02 × 10 23 = 2.4 × 10 23 molecules Q2: An ideal gas mixture filled inside a balloon expands according to the relation ???? ?? /?? = constant. The temperature inside the balloon is (A) Increasing (B) Decreasing (C) Constant (D) Can't be said Ans: (A) PV 2/3 = const. ? nRT V V 2/3 = const. ? TV -1/3 = const. ? T = conts. × V 1/3 ? On increasing volume, temperature increase Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen supplied to the tank is: (A) ?? ???? (B) ???? ???? (C) ???? ???? (D) ???? ???? Ans: (C) T = constant, V = constant, ?? ?? = 35 28 = 1.25 Kmoles ? ?? ?? = ???? ?? = const. ? ?? ?? ?? ?? = ?? ?? ?? ?? ? ?? ?? = ?? ?? ?? ?? × ?? ?? = 9 6 × 35 28 ˜ 1.875 kmoles ? Moles of O 2 supplied = 1.875 - 1.25 = 0.625kmoles ? Amount of oxygen = 20 kg Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to maintained original pressure. The temperature ?? is equal to (A) ?????? ?? (B) ?????? ?? (C) ?????? ?? (D) ???? ?? Ans: (B) ???? = 4 ?? ???? ???? = ( 4 - 0.8) ?? ?? ( ?? + 50) = 3.2?? ?? ( ?? + 50) By (i) and (ii) we get, 4 ?? ???? = 3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50 ? ?? = 200 ?? Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ???? ° ?? the pressure is found to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5 atmosphere. The ratio of the molecular weights of these gases will be (A) ?? : ?? (B) 3:1 (C) ?? : ?? (D) ?? : ?? Ans: (A) For P = 1 atm , m 1 = 2gms , T = 298 K ? 1 × ?? = 2?? ?? 1 × 298 For ?? = 1.5 atm, ?? 1 = 2gm , ?? 2 = 3gm , ?? = 298 K. ? 1.5 × ?? = [ 2 ?? 1 + 3 ?? 2 ] ?? × 298 Using (ii)/(i) we get, 1.5 = [ 2 ?? 1 + 2 ?? 2 ] 2 ?? 1 ? 3 = [2 + 3?? 1 ?? 2 ] ? ?? 1 ?? 2 = 1 3 Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? , then its temperature will be? (A) T (B) v ?? ?? (C) ?? ?? (D) ?? v ?? ?? Ans: (B) ?? = ?????? ?? ? ( ?????? ?? ) 2 ?? = constant ? ?? 2 ?? = constant ? ?? ?? = ( ?? ?? ?? ?? ) 1 2 × ?? ?? = v 2?? Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only ???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ???? of mercury, what is the pressure at the top of the tube? (A) ???? . ???????? (B) ???? . ???????? (C) ?? . ?????????? (D) ?? . ?????????? Ans: (A) ?? at top of tube + ?? due to 50 cm of Hg = ?? atmospheric ? ?? at top of tube = ( 75 - 50) cm of Hg = 25 cm of Hg = 25 × 10 5 75 Pa = 33.3kPa Page 4 JEE Solved Example on Thermodynamics JEE Mains Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? ° ?? at ?? . ?? × ???? ?? ???????????? (A) ?? . ?? × ???? ???? (B) ?? × ???? ???? (C) ?? × ???? ???? (D) ?? . ?? × ???? ???? Ans: (A) ?? = 7 L = 7 × 10 -3 m 3 ?? = 273 K P = 1.3 × 10 5 Pa ? m = PV RT = 1.3 × 10 5 × 7 × 10 -3 8.314 × 273 ? 0.4 moles ? No. of molecules = 0.4 × 6.02 × 10 23 = 2.4 × 10 23 molecules Q2: An ideal gas mixture filled inside a balloon expands according to the relation ???? ?? /?? = constant. The temperature inside the balloon is (A) Increasing (B) Decreasing (C) Constant (D) Can't be said Ans: (A) PV 2/3 = const. ? nRT V V 2/3 = const. ? TV -1/3 = const. ? T = conts. × V 1/3 ? On increasing volume, temperature increase Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen supplied to the tank is: (A) ?? ???? (B) ???? ???? (C) ???? ???? (D) ???? ???? Ans: (C) T = constant, V = constant, ?? ?? = 35 28 = 1.25 Kmoles ? ?? ?? = ???? ?? = const. ? ?? ?? ?? ?? = ?? ?? ?? ?? ? ?? ?? = ?? ?? ?? ?? × ?? ?? = 9 6 × 35 28 ˜ 1.875 kmoles ? Moles of O 2 supplied = 1.875 - 1.25 = 0.625kmoles ? Amount of oxygen = 20 kg Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to maintained original pressure. The temperature ?? is equal to (A) ?????? ?? (B) ?????? ?? (C) ?????? ?? (D) ???? ?? Ans: (B) ???? = 4 ?? ???? ???? = ( 4 - 0.8) ?? ?? ( ?? + 50) = 3.2?? ?? ( ?? + 50) By (i) and (ii) we get, 4 ?? ???? = 3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50 ? ?? = 200 ?? Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ???? ° ?? the pressure is found to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5 atmosphere. The ratio of the molecular weights of these gases will be (A) ?? : ?? (B) 3:1 (C) ?? : ?? (D) ?? : ?? Ans: (A) For P = 1 atm , m 1 = 2gms , T = 298 K ? 1 × ?? = 2?? ?? 1 × 298 For ?? = 1.5 atm, ?? 1 = 2gm , ?? 2 = 3gm , ?? = 298 K. ? 1.5 × ?? = [ 2 ?? 1 + 3 ?? 2 ] ?? × 298 Using (ii)/(i) we get, 1.5 = [ 2 ?? 1 + 2 ?? 2 ] 2 ?? 1 ? 3 = [2 + 3?? 1 ?? 2 ] ? ?? 1 ?? 2 = 1 3 Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? , then its temperature will be? (A) T (B) v ?? ?? (C) ?? ?? (D) ?? v ?? ?? Ans: (B) ?? = ?????? ?? ? ( ?????? ?? ) 2 ?? = constant ? ?? 2 ?? = constant ? ?? ?? = ( ?? ?? ?? ?? ) 1 2 × ?? ?? = v 2?? Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only ???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ???? of mercury, what is the pressure at the top of the tube? (A) ???? . ???????? (B) ???? . ???????? (C) ?? . ?????????? (D) ?? . ?????????? Ans: (A) ?? at top of tube + ?? due to 50 cm of Hg = ?? atmospheric ? ?? at top of tube = ( 75 - 50) cm of Hg = 25 cm of Hg = 25 × 10 5 75 Pa = 33.3kPa Q. 8 A vessel contains 1 mole of ?? ?? gas (molar mass 32) at a temperature ?? . The pressure of the gas is ?? . An identical vessel containing one mole of He gas (molar mass 4) at a temperature ?? ?? has a pressure of (A) ?? /?? (B) ?? (C) ?? ?? (D) ???? Ans: (C) Q9: The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule temperature ?? is (A) 3 (B) ?? /?? (C) ?? /?? (D) ?? /?? Ans: (D) For diatomic molecule Translational degree of freedoms = 3 Rotational degree of freedoms = 2 Ratio = 3???? 2???? = 3 2 Page 5 JEE Solved Example on Thermodynamics JEE Mains Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? ° ?? at ?? . ?? × ???? ?? ???????????? (A) ?? . ?? × ???? ???? (B) ?? × ???? ???? (C) ?? × ???? ???? (D) ?? . ?? × ???? ???? Ans: (A) ?? = 7 L = 7 × 10 -3 m 3 ?? = 273 K P = 1.3 × 10 5 Pa ? m = PV RT = 1.3 × 10 5 × 7 × 10 -3 8.314 × 273 ? 0.4 moles ? No. of molecules = 0.4 × 6.02 × 10 23 = 2.4 × 10 23 molecules Q2: An ideal gas mixture filled inside a balloon expands according to the relation ???? ?? /?? = constant. The temperature inside the balloon is (A) Increasing (B) Decreasing (C) Constant (D) Can't be said Ans: (A) PV 2/3 = const. ? nRT V V 2/3 = const. ? TV -1/3 = const. ? T = conts. × V 1/3 ? On increasing volume, temperature increase Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen supplied to the tank is: (A) ?? ???? (B) ???? ???? (C) ???? ???? (D) ???? ???? Ans: (C) T = constant, V = constant, ?? ?? = 35 28 = 1.25 Kmoles ? ?? ?? = ???? ?? = const. ? ?? ?? ?? ?? = ?? ?? ?? ?? ? ?? ?? = ?? ?? ?? ?? × ?? ?? = 9 6 × 35 28 ˜ 1.875 kmoles ? Moles of O 2 supplied = 1.875 - 1.25 = 0.625kmoles ? Amount of oxygen = 20 kg Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to maintained original pressure. The temperature ?? is equal to (A) ?????? ?? (B) ?????? ?? (C) ?????? ?? (D) ???? ?? Ans: (B) ???? = 4 ?? ???? ???? = ( 4 - 0.8) ?? ?? ( ?? + 50) = 3.2?? ?? ( ?? + 50) By (i) and (ii) we get, 4 ?? ???? = 3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50 ? ?? = 200 ?? Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ???? ° ?? the pressure is found to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5 atmosphere. The ratio of the molecular weights of these gases will be (A) ?? : ?? (B) 3:1 (C) ?? : ?? (D) ?? : ?? Ans: (A) For P = 1 atm , m 1 = 2gms , T = 298 K ? 1 × ?? = 2?? ?? 1 × 298 For ?? = 1.5 atm, ?? 1 = 2gm , ?? 2 = 3gm , ?? = 298 K. ? 1.5 × ?? = [ 2 ?? 1 + 3 ?? 2 ] ?? × 298 Using (ii)/(i) we get, 1.5 = [ 2 ?? 1 + 2 ?? 2 ] 2 ?? 1 ? 3 = [2 + 3?? 1 ?? 2 ] ? ?? 1 ?? 2 = 1 3 Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? , then its temperature will be? (A) T (B) v ?? ?? (C) ?? ?? (D) ?? v ?? ?? Ans: (B) ?? = ?????? ?? ? ( ?????? ?? ) 2 ?? = constant ? ?? 2 ?? = constant ? ?? ?? = ( ?? ?? ?? ?? ) 1 2 × ?? ?? = v 2?? Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only ???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ???? of mercury, what is the pressure at the top of the tube? (A) ???? . ???????? (B) ???? . ???????? (C) ?? . ?????????? (D) ?? . ?????????? Ans: (A) ?? at top of tube + ?? due to 50 cm of Hg = ?? atmospheric ? ?? at top of tube = ( 75 - 50) cm of Hg = 25 cm of Hg = 25 × 10 5 75 Pa = 33.3kPa Q. 8 A vessel contains 1 mole of ?? ?? gas (molar mass 32) at a temperature ?? . The pressure of the gas is ?? . An identical vessel containing one mole of He gas (molar mass 4) at a temperature ?? ?? has a pressure of (A) ?? /?? (B) ?? (C) ?? ?? (D) ???? Ans: (C) Q9: The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule temperature ?? is (A) 3 (B) ?? /?? (C) ?? /?? (D) ?? /?? Ans: (D) For diatomic molecule Translational degree of freedoms = 3 Rotational degree of freedoms = 2 Ratio = 3???? 2???? = 3 2 Q10 : One mole of an ideal gas at STP is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by factor. (A) 1.5 (B) v ?? (C) 2 (D) 4 Ans: (D) We know ?? rms = 1.085v avg ? v 3?? ?? = 1.085v avg ; ?? is density In this case ?? is constant ? ?? ? ( ?? avg ) 2 ? ?? ?? ?? ?? = [ ( ?? avg ) ?? ( ?? avg ) ?? ] 2 = 4 Q11: One mole of an ideal gas is contained within a cylinder by a frictionless piston and is initially at temperature ?? . The pressure of the gas is kept constant while it is heated and its volume doubles. If ?? is molar gas constant, the work done by the gas in increasing its volume is? (A) ???? ???? ?? (B) ?? /?? RT (C) RT (D) ?? /?? RT Ans: (C) Frictionless piston means, no generation of heat due to the motion of piston. n = 1 T i = T P = const. ?? i = V ?? f = 2 V Initially: - ???? = ???? Work done = P?V = P( 2 V - V) = PV = RT Q12: A polyatomic gas with six degrees of freedom does ???? ?? work when it is expanded at constant pressure. The heat given to the gas is? (A) ?????? ?? (B) ?????? ?? (C) ?????? ?? (D) ?????? ?? Ans: (A) ?? = 6Read More
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FAQs on Solved Example: Thermodynamics - Physics for JEE Main & Advanced
| 1. What is the first law of thermodynamics? |  |
Ans. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. It is also known as the law of conservation of energy.
| 2. Can you explain the difference between heat and temperature in thermodynamics? | |
Ans. Heat is the transfer of energy between two systems due to a temperature difference, while temperature is a measure of the average kinetic energy of the particles in a system.
| 3. What is entropy in thermodynamics? | |
Ans. Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic quantity that increases in the direction of spontaneous change and is related to the second law of thermodynamics.
| 4. How does the second law of thermodynamics affect the efficiency of heat engines? | |
Ans. The second law of thermodynamics states that heat will naturally flow from a hot object to a cold object, and that no process is 100% efficient. This means that heat engines cannot convert all of the input heat into work, leading to limitations on their efficiency.
| 5. Can you provide an example of a thermodynamic process in everyday life? | |
Ans. An example of a thermodynamic process in everyday life is the operation of a refrigerator. The refrigerator works by removing heat from the inside to the outside, using a refrigeration cycle based on the principles of thermodynamics.
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