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
What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?
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 substance which allows heat radiations to pass through is _______.
(A) iron
(B) water vapour
(C) wood
(D) dry air
A body cools from 80° C to 70° C in 5 minutes and to 62° C in the next 5 minutes. Calculate the temperature of the surroundings.
It is said that mercury is used in defining the temperature scale because it expands uniformly with temperature. If the temperature scale is not yet defined, is it logical to say that a substance expands uniformly with temperature?
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?
Which of the curves in the following figure represents the relation between Celsius and Fahrenheit temperatures?
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
An aluminium sphere is dipped into water at 10°C. If the temperature is increased, the force of buoyancy
A spinning wheel is brought in contact with an identical wheel spinning at identical speed. The wheels slow down under the action of friction. Which of the following energies of the first wheel decreases?
(a) Kinetic
(b) Total
(c) Mechanical
(d) Internal
Is heat a conserved quantity?
As the temperature is increased, the time period of a pendulum
When a solid melts or a liquid boils, the temperature does not increase even when heat is supplied. Where does the energy go?
A person's skin is more severely burnt when put in contact with 1 g of steam at 100°C than when put in contact with 1 g of water at 100°C. Explain
Water equivalent of a body is measured in ___________ .
The heat capacity of a body depends on
(a) the heat given
(b) the temperature raised
(c) the mass of the body
(d) the material of the body
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 circular hole of diameter 2.00 cm is made in an aluminium plate at 0°C. What will be the diameter at 100°C? α for aluminium = 2.3 × 10–5 °C–1.
The volume of a glass vessel is 1000 cc at 20°C. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are 1.8 × 10–6 °C–1 and 9.0 × 10–6 °C–1 , respectively.
A steel ball that is initially at a pressure of 1.0 × 105 Pa is heated from 20°C to 120°C, keeping its volume constant.
Find the pressure inside the ball. Coefficient of linear expansion of steel = 12 × 10–6 °C–1and bulk modulus of steel = 1.6 × 1011 Nm–2.
Define one mole.
Two objects are said to be in thermal contact if they can exchange heat energy.
Temperature in the form of energy.
Analogy
Evaporation:: 100°C: Freezing:: ______.
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.
Near the melting point of a solid, the heat supplied does NOT raise the temperature. Instead, what does it do?
The concept of thermal equilibrium, where heat flows between bodies until they reach the same temperature, is the basis of which law of thermodynamics?
