Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Heat and Thermodynamics question

2017 · Shift 0 · Q59
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Heat and Thermodynamics
  5. /2017 · Shift 0 · Q59

Heat and Thermodynamics question

2017 · Shift 0 · Q59

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by: (Given : room temperature = 30oC, specific heat of copper = 0.1 cal/gmoC)
  1. A
    825oC
  2. B
    800oC
  3. C
    885oC
  4. D
    1250oC
View written solutionFree

Correct answer: C

  1. Given data
  • Mass of hot copper ball: mb=100 gm_b = 100\,\text{g}mb​=100g
  • Initial temperature of ball: TTT
  • Mass of copper calorimeter: mc=100 gm_c = 100\,\text{g}mc​=100g
  • Mass of water: mw=170 gm_w = 170\,\text{g}mw​=170g
  • Initial room temperature: 30∘C30^\circ \text{C}30∘C
  • Final temperature of system: 75∘C75^\circ \text{C}75∘C
  • Specific heat of copper: sc=0.1 cal g−1 ∘C−1s_c = 0.1\,\text{cal g}^{-1}\,{}^\circ\text{C}^{-1}sc​=0.1cal g−1∘C−1
  • Specific heat of water: sw=1 cal g−1 ∘C−1s_w = 1\,\text{cal g}^{-1}\,{}^\circ\text{C}^{-1}sw​=1cal g−1∘C−1
  1. Principle used

Since no heat is lost to surroundings,

Heat lost by hot copper ball=Heat gained by water+Heat gained by calorimeter\text{Heat lost by hot copper ball} = \text{Heat gained by water} + \text{Heat gained by calorimeter}Heat lost by hot copper ball=Heat gained by water+Heat gained by calorimeter

  1. Heat lost by copper ball

The ball cools from TTT to 75∘C75^\circ\text{C}75∘C.

Qlost=mbsc(T−75)=100×0.1×(T−75)=10(T−75)Q_{\text{lost}} = m_b s_c (T-75) = 100 \times 0.1 \times (T-75) = 10(T-75)Qlost​=mb​sc​(T−75)=100×0.1×(T−75)=10(T−75)

  1. Heat gained by water

Water warms from 30∘C30^\circ\text{C}30∘C to 75∘C75^\circ\text{C}75∘C.

Qw=mwsw(75−30)=170×1×45=7650 calQ_{w} = m_w s_w (75-30) = 170 \times 1 \times 45 = 7650\,\text{cal}Qw​=mw​sw​(75−30)=170×1×45=7650cal

  1. Heat gained by copper calorimeter

Calorimeter also warms from 30∘C30^\circ\text{C}30∘C to 75∘C75^\circ\text{C}75∘C.

Qc=mcsc(75−30)=100×0.1×45=450 calQ_{c} = m_c s_c (75-30) = 100 \times 0.1 \times 45 = 450\,\text{cal}Qc​=mc​sc​(75−30)=100×0.1×45=450cal

  1. Apply heat balance

10(T−75)=7650+45010(T-75) = 7650 + 45010(T−75)=7650+450

10(T−75)=810010(T-75) = 810010(T−75)=8100

T−75=810T-75 = 810T−75=810

T=885∘CT = 885^\circ\text{C}T=885∘C

  1. Check options
  • A: 825∘C825^\circ\text{C}825∘C — incorrect
  • B: 800∘C800^\circ\text{C}800∘C — incorrect
  • C: 885∘C885^\circ\text{C}885∘C — correct
  • D: 1250∘C1250^\circ\text{C}1250∘C — incorrect

Therefore, the correct option is C.

PreviousNext

More from Heat and Thermodynamics

  • A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature,…2016 · MCQ
  • The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :2016 · MCQ
  • 200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :2016 · MCQ
  • Which of the following shows the correct relationship between the pressure ‘P’ and density ρ of an ideal gas at constant temperature ?2016 · MCQ
  • ′n′ moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be : Includes diagram2016 · MCQ
  • An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn= constant, then n is given by (Here…2016 · MCQ
  • A pendulum clock loses 12s a day if the temperature is 40∘C and gains 4s a day if the temperature is 20∘C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α)…2016 · MCQ
  • Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u=VU​∝T4 and pressure p=31​(VU​)…2015 · MCQ