A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.
B. Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15.
C. A carnot Engine working between 100 K and 400 K has an efficiency of 75%.
D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.
Choose the correct answer from the options given below
To determine which of the statements are correct, let's analyze each one step by step:
Statement A: "When the small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice."
This statement refers to Newton's Law of Cooling, which states that the rate of loss of heat of a body is directly proportional to the difference in temperature between the body and its surroundings, q \propto \Delta T.
Thus, if the temperature difference is doubled, the rate of heat loss also doubles. Hence, this statement is correct.
Statement B: "Two bodies P and Q having equal surface areas are maintained at temperatures 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15."
The Stefan-Boltzmann Law states that the power emitted by a black body per unit area is directly proportional to the fourth power of the temperature: E = \sigma T^4.
To find the ratio of thermal radiation emitted, convert the temperatures to Kelvin: 10°C = 283 K and 20°C = 293 K.
The ratio of emitted power is \frac{293^4}{283^4} \approx 1.15. Hence, this statement is correct.
Statement C: "A Carnot Engine working between 100 K and 400 K has an efficiency of 75%."
The efficiency of a Carnot Engine is given by \eta = 1 - \frac{T_C}{T_H}, where T_C is the cold reservoir temperature and T_H is the hot reservoir temperature.
Substituting the values: \eta = 1 - \frac{100}{400} = 1 - 0.25 = 0.75 or 75%.
Therefore, this statement is correct.
Statement D: "When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice."
According to Newton's Law of Cooling, if the temperature difference is quadrupled, the rate of heat loss should also quadruple, not double.
Thus, this statement is incorrect.
Based on the analysis, the correct statements are A, B, and C. Therefore, the correct answer is A, B, C only.
