1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Morning Slot

Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/oC Specific heat of Ice = 2.1J/g/oC Heat of fusion of water at 0oC= 334J/g)
A
100 g
B
60 g
C
50 g
D
40 g

Explanation

Let amount of ice is m gm.

According to principal of calorimeter heat taken by ice = heat given by water

$$ \therefore $$  20 $$ \times $$ 2.1 $$ \times $$ m + (m $$-$$ 20) $$ \times $$ 334

= 50 $$ \times $$ 4.2 $$ \times $$ 40

376 m = 8400 + 6680

m = 40.1
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
A
200oC
B
270oC
C
230oC
D
250oC

Explanation

$$\Delta {\ell _1} = \Delta {\ell _2}$$

$$\ell {\alpha _1}\Delta {T_1} = \ell {\alpha _2}\Delta {T_2}$$

$${{{\alpha _1}} \over {{\alpha _2}}} = {{\Delta {T_1}} \over {\Delta {T_2}}}$$

$${4 \over 3} = {{T - 30} \over {180 - 30}}$$

$$T = {230^o}C$$
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :
A
60oC
B
70oC
C
85oC
D
80oC

Explanation

100 $$ \times $$ SA $$ \times $$ [100 $$-$$ 90] = 50 $$ \times $$ SB $$ \times $$ (90 $$-$$ 75)

2SA = 1.5 SB

SA = $${3 \over 4}$$SB

Now, 100 $$ \times $$ SA $$ \times $$ [100 $$-$$ T] = 50 $$ \times $$ SB (T $$-$$ 50)

2 $$ \times $$ $$\left( {{3 \over 4}} \right)$$ (100 $$-$$ T) = (T $$-$$ 50)

300 $$-$$ 3T = 2T $$-$$ 100

400 = 5T

T = 80
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads x0/2 ?
A
60
B
35
C
25
D
40

Explanation



$$ \Rightarrow $$   ToC = $${{{x_0}} \over 6}$$ & $$\left( {{x_0} - {{{x_0}} \over 3}} \right)$$ = (100 $$-$$ 0oC)

x0 = $${{300} \over 2}$$

$$ \Rightarrow $$  ToC = $${{150} \over 6}$$ = 25oC

Questions Asked from Heat and Thermodynamics

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