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A liquid of mass m and specific heat S is heated to a temperature T. Another liquid of mass m/2 and specific heat 2S is heated to a temperature 2T. If these two liquids are mixed, the resultant temperature of the mixture
- a)2/3 T
- b)8/5 T
- c)3/3 T
- d)3/2 T
Correct answer is option 'D'. Can you explain this answer?
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A liquid of mass m and specific heat S is heated to a temperature T. A...
Given:
- Mass of first liquid = m
- Specific heat of first liquid = S
- Temperature of first liquid = T
- Mass of second liquid = m/2
- Specific heat of second liquid = 2S
- Temperature of second liquid = 2T
To find: Resultant temperature of mixture.
Solution:
Let the resultant temperature of the mixture be x.
Heat gained by first liquid = m × S × (x - T)
Heat gained by second liquid = (m/2) × 2S × (x - 2T) = m × S × (x - 2T)
As per the law of conservation of energy, the heat gained by the two liquids must be equal to the heat lost by the mixture.
Heat lost by mixture = Heat gained by first liquid + Heat gained by second liquid
= mS(x - T) + mS(x - 2T)
= 2mS(x - T)
Equating the two, we get:
2mS(x - T) = m × S × (x - 2T) + mS(x - T)
Simplifying, we get:
2x - 2T = x - 2T + x - T
Solving for x, we get:
x = (3T + 2T)/2 = 5T/2
Therefore, the resultant temperature of the mixture is 5T/2 or 2.5T, which is option D.
- Mass of first liquid = m
- Specific heat of first liquid = S
- Temperature of first liquid = T
- Mass of second liquid = m/2
- Specific heat of second liquid = 2S
- Temperature of second liquid = 2T
To find: Resultant temperature of mixture.
Solution:
Let the resultant temperature of the mixture be x.
Heat gained by first liquid = m × S × (x - T)
Heat gained by second liquid = (m/2) × 2S × (x - 2T) = m × S × (x - 2T)
As per the law of conservation of energy, the heat gained by the two liquids must be equal to the heat lost by the mixture.
Heat lost by mixture = Heat gained by first liquid + Heat gained by second liquid
= mS(x - T) + mS(x - 2T)
= 2mS(x - T)
Equating the two, we get:
2mS(x - T) = m × S × (x - 2T) + mS(x - T)
Simplifying, we get:
2x - 2T = x - 2T + x - T
Solving for x, we get:
x = (3T + 2T)/2 = 5T/2
Therefore, the resultant temperature of the mixture is 5T/2 or 2.5T, which is option D.
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A liquid of mass m and specific heat S is heated to a temperature T. A...
Use heat loss =heat gained by body
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A liquid of mass m and specific heat S is heated to a temperature T. Another liquid of mass m/2 and specific heat 2S is heated to a temperature 2T. If these two liquids are mixed, the resultant temperature of the mixturea)2/3 Tb)8/5 Tc)3/3 Td)3/2 TCorrect answer is option 'D'. Can you explain this answer?
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