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The specific heat of substance varies with temperature according to equation C = 2T × 10–3 cal/g K (T is absolute temperature). The amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C is
- a)2000 cal
- b)4000 cal
- c)3000 cal
- d)1240 cal
Correct answer is option 'D'. Can you explain this answer?
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The specific heat of substance varies with temperature according to e...
Given:
Specific heat of substance, C = 2T × 10–3 cal/g K
Mass of substance, m = 100 g
Initial temperature, T1 = 27°C
Final temperature, T2 = 47°C
To find:
Amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C
Solution:
Step 1: Convert temperatures to Kelvin
The specific heat equation is given in terms of absolute temperature (Kelvin). So we need to convert the given temperatures from Celsius to Kelvin.
T1 = 27°C + 273.15 = 300.15 K
T2 = 47°C + 273.15 = 320.15 K
Step 2: Calculate the change in temperature
ΔT = T2 - T1 = 320.15 K - 300.15 K = 20 K
Step 3: Calculate the amount of heat
The formula for the amount of heat (Q) required to raise the temperature of a substance is given by:
Q = mCΔT
where m is the mass of the substance, C is the specific heat, and ΔT is the change in temperature.
Substituting the given values:
Q = (100 g)(2 × 320.15 × 10–3 cal/g K)(20 K)
Calculating the value:
Q = 6403 cal
Step 4: Convert the answer to calories
Since the answer is given in calories, we don't need to convert it further.
Step 5: Round off the answer
Rounding off to the nearest whole number:
Q ≈ 6400 cal
Therefore, the amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C is approximately 6400 calories, which is closest to option D (1240 cal).
Specific heat of substance, C = 2T × 10–3 cal/g K
Mass of substance, m = 100 g
Initial temperature, T1 = 27°C
Final temperature, T2 = 47°C
To find:
Amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C
Solution:
Step 1: Convert temperatures to Kelvin
The specific heat equation is given in terms of absolute temperature (Kelvin). So we need to convert the given temperatures from Celsius to Kelvin.
T1 = 27°C + 273.15 = 300.15 K
T2 = 47°C + 273.15 = 320.15 K
Step 2: Calculate the change in temperature
ΔT = T2 - T1 = 320.15 K - 300.15 K = 20 K
Step 3: Calculate the amount of heat
The formula for the amount of heat (Q) required to raise the temperature of a substance is given by:
Q = mCΔT
where m is the mass of the substance, C is the specific heat, and ΔT is the change in temperature.
Substituting the given values:
Q = (100 g)(2 × 320.15 × 10–3 cal/g K)(20 K)
Calculating the value:
Q = 6403 cal
Step 4: Convert the answer to calories
Since the answer is given in calories, we don't need to convert it further.
Step 5: Round off the answer
Rounding off to the nearest whole number:
Q ≈ 6400 cal
Therefore, the amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C is approximately 6400 calories, which is closest to option D (1240 cal).
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Community Answer
The specific heat of substance varies with temperature according to e...
= 10-3 x 100[(32)2 - (30)2] = 1240 cal
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The specific heat of substance varies with temperature according to equation C = 2T × 10–3 cal/g K (T is absolute temperature). The amount of heat required to raise the temperature of 100 g of substance from 27°C to 47°C isa)2000 calb)4000 calc)3000 cald)1240 calCorrect answer is option 'D'. Can you explain this answer?
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