Advertisements
Advertisements
Question
A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45°C if the temperature of surroundings is 25°C.
Advertisements
Solution
Given that for the metal sphere
`((d theta)/dt)_1=4^@`C/min,
`theta_1=50^@C, theta_2=45^@ and theta_0=25^C`
By Newton's law of cooling,
`((d theta)/dt)=k(theta-theta_0)`
`therefore((d theta)/dt)_1/((d theta)/dt)_2=((theta_1-theta_0))/((theta_2-theta_0)`
`therefore((d theta)/dt)_1/((d theta)/dt)_2=((50^@-25^0))/((45^@-25^@)`
`therefore ((d theta)/dt)_2=20^@/25^@*((d theta)/dt)_1=20^@/25^@*4=3.2`
`therefore ((d theta)/dt)_2=3.2^@`C/min
APPEARS IN
RELATED QUESTIONS
A pinhole is made in a hollow sphere of radius 5 cm whose inner wall is at temperature 727oC. Find the power radiated per unit area. [Stefan’s constant σ = 5.7 x 10-8 J/m2 s K4 , emissivity (e) = 0.2]
A metal ball cools from 64 °C to 50 °C in 10 minutes and to 42 °C in next 10 minutes. The ratio of rates of fall of temperature during the two intervals is _______.
A body cools from 62°C to 54°C in 10 minutes and to 48°C in the next 10 minutes. Find the temperature of the surroundings.
The susceptibility of magnesium at 300K is 1.2 x 10-5. At what temperature will the susceptibility increase to 1.8 X 10-5?
Why do marine animals live deep inside a lake when the surface of the lake freezes?
The length of a brass rod is found to be less on a hot summer day than on a cold winter day as measured by the same aluminium scale. Can we conclude that brass shrinks on heating?
The density of water at 4°C is supposed to be 1000 kg m–3. Is it same at sea level and at high altitude?
Which of the following pairs may give equal numerical values of the temperature of a body?
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a line parallel to itself will increase by
In a calorimeter, the heat given by the hot object is assumed to be equal to the heat taken by the cold object. Does it mean that heat of the two objects taken together remains constant?
Which of the following pairs of physical quantities may be represented in the same unit?
Two bodies at different temperatures are mixed in a calorimeter. Which of the following quantities remains conserved?
A resistance thermometer reads R = 20.0 Ω, 27.5 Ω, and 50.0 Ω at the ice point (0°C), the steam point (100°C) and the zinc point (420°C), respectively. Assuming that the resistance varies with temperature as Rθ = R0 (1 + αθ + βθ2), find the values of R0, α and β. Here θ represents the temperature on the Celsius scale.
A concrete slab has a length of 10 m on a winter night when the temperature is 0°C. Find the length of the slab on a summer day when the temperature is 35°C. The coefficient of linear expansion of concrete is 1.0 × 10–5 °C–1.
A metre scale made of steel is calibrated at 20°C to give correct reading. Find the distance between the 50 cm mark and the 51 cm mark if the scale is used at 10°C. Coefficient of linear expansion of steel is 1.1 × 10–5 °C–1.
A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two such sections, so that there is no compression during summer when the maximum temperature rises to 48°C? Coefficient of linear expansion of iron = 11 × 10–6 °C–1.
A steel wire of cross-sectional area 0.5 mm2 is held between two fixed supports. If the wire is just taut at 20°C, determine the tension when the temperature falls to 0°C. Coefficient of linear expansion of steel is 1.2 × 10–5 °C–1 and its Young's modulus is 2.0 × 10–11 Nm–2.
‘An object contains more heat’- is it a right statement? If not why?
Explain the meaning of heat and work with suitable examples.
Temperature and Heat are ______
Temperature in the form of energy.
The normal temperature of our body is 37°C.
The degree of hotness and coldness of a body is called ______.
An earthen pitcher loses 1 gm of water per minute due to evaporation. If the water equivalent of the pitcher is 0.5 kg and the pitcher contains 9.5 kg of water, calculate the time required for the water in a pitcher to cool to 28°C from the original temperature of 30°C. Neglect radiation effects. The latent heat of vaporization in this range of temperature is 580 Cal/gm and the specific heat of water is 1 Cal/gm°C.
The temperature of a liquid drops from 365 K to 361 K in 2 min. Find the time during which the temperature of the liquid drops from 344 K to 342 K.
(Take, room temperature = 293 K)
What physical quantity does temperature primarily indicate?
