Question

If heat Q is required to increase the temperature of a metal object from 4 ∘C to 7∘C, the amount of heat necessary to increase its temperature from 7 ∘C to 19 ∘C is most likely If heat is required to increase the temperature of a metal object from 4 to 7, the amount of heat necessary to increase its temperature from 7 to 19 is most likely 4 Q. Q. 5 Q. 3 Q.

Answer 1

Answer:

4Q

Explanation:

Case 1 :

$m$ = mass of the metal

$c$ = specific heat of the metal

$\Delta T$ = Change in temperature = 7 - 4 = 3 C

Amount of heat required for the above change of temperature is given as

$Q = m c \Delta T\\Q = m c (7 - 4)\\Q = 3 m c$

Case 2 :

$m$ = mass of the metal

$c$ = specific heat of the metal

$\Delta T$ = Change in temperature = 19 - 7 = 12 C

Amount of heat required for the above change of temperature is given as

$Q' = m c \Delta T\\Q' = m c (12)\\Q' = (4)(3 m c)\\Q' = 4Q$

Hence the correct choice is

4Q

Answer 2

Answer:

So in order to increase the temperature of the material from 7° C to 19°C, heat required to the material is is 3 Q

Explanation:

We know temperature is directly proportional to amount of heat applied to the substance.

Q = mcdT

Q = heat supplied

m=mass of the substance

c= specific heat capacity

dT= increase in temperature

Let let us consider two situations as dQ_1 and dQ_2

Therefore,

$\frac{Q_1}{Q_2}= \frac{dT_1}{dT_2}$

$\frac{Q_1}{Q_2}= \frac{7-3}{19-7}$

$\frac{Q_1}{Q_2}= \frac{4}{12}$

$\frac{Q_1}{Q_2}= \frac{1}{3}$

Q1=Q

then,   Q2 = 3Q

So in order to increase the temperature of the material from 7° C to 19°C, heat required to the material is is 3 Q