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Learn/ 9th Physics/ Unit 7 /Numericals

Unit 7: Thermal Properties of Matter — Numericals

9th Class Physics · Unit 7: Thermal Properties of Matter

7.1.The temperature of normal human body on Fahrenheit scale is 98.6°F. Convert it into Celsius scale and Kelvin scale.
Given
Temperature in Fahrenheit F = 98.6°F
Formula
Celsius conversion C = F - 321.8
Kelvin conversion T(k) = 273 + C
Working
Substitute into Celsius formula C = 98.6 - 321.8 = 66.61.8
Result
Temperature in Celsius C = 37°C
Working
Substitute into Kelvin formula T(k) = 273 + 37
Result
Temperature in Kelvin T(k) = 310 K
7.2.At what temperature Celsius and Fahrenheit thermometer reading would be the same?
Given
Condition TF = TC = T
Formula
Fahrenheit-Celsius relation TF = 95TC + 32
Set equal T = 95T + 32
Rearrange T - 95T = 32
Factor Tleft(1 - 95right) = 32
Simplify Tleft(5 - 95right) = 32
Simplify Tleft(-45right) = 32
Working
Solve for T T = 32 × 5-4 = 160-4
Result
Temperature T = -40°C
7.3.Convert 5°F to Celsius and Kelvin scale.
Given
Temperature in Fahrenheit F = 5°F
Formula
Celsius conversion C = F - 321.8
Kelvin conversion T(k) = C + 273
Working
Substitute into Celsius formula C = 5 - 321.8 = -271.8
Result
Temperature in Celsius C = -15°C
Working
Substitute into Kelvin formula T(k) = -15 + 273
Result
Temperature in Kelvin T(k) = 258 K
7.4.What is equivalent temperature of 25°C on Fahrenheit and Kelvin scales?
Given
Temperature in Celsius C = 25°C
Formula
Kelvin conversion T(k) = C + 273
Fahrenheit conversion F = 1.8C + 32
Working
Substitute into Kelvin formula T(k) = 25 + 273
Result
Temperature in Kelvin T(k) = 298 K
Working
Substitute into Fahrenheit formula F = 1.8(25) + 32 = 45 + 32
Result
Temperature in Fahrenheit F = 77°F
7.5.The ice and steam points on an ungraduated thermometer are found to be 192 mm apart. What temperature will be on Celsius scale if the length of mercury thread is at 67.2 mm above the ice point mark?
Given
Difference between ice and steam points Distance = 192 mm
Mercury thread above ice point Length above ice point = 67.2 mm
Formula
Change per mm Change per mm = 100192
Working
Calculate change per mm 100192 = 0.52083
Given
Temperature at steam point T_{steam = 100°C
Temperature above ice point T = 67.2 × 0.52083
Result
Temperature in Celsius T = 35°C
7.6.The length between the fixed point of liquid-in-glass thermometer is 20 cm. if the mercury level is 4.5 cm above the lower mark, what is the temperature on the Fahrenheit scale?
Given
Length between fixed points L = 20 cm
Mercury level above lower mark h = 4.5 cm
Formula
Change per cm Change per cm = 10020
Working
Calculate change per cm 10020 = 5
Temperature in Celsius TC = 5 × 4.5
Result
Temperature in Celsius TC = 22.5°C
Formula
Fahrenheit conversion F° = 1.8°C + 32
Working
Substitute into Fahrenheit formula F° = 1.8(22.5) + 32 = 40.5 + 32
Result
Temperature in Fahrenheit F° = 72.5°F