Chapter 7: Thermal Properties of MatterNumericals Solved Step by Step
All 6 numericals of 9th Class Physics Chapter 7, Thermal Properties of Matter, solved step by step: Given Data, To Find, Formula, Calculation and Result, the way you write them in the exam. Punjab Board new syllabus.
Each numerical in the order you write it in the exam: Given Data, To Find, Formula, Calculation, Result.
Numerical 7.1
Normal human body temperature is 98.6 °F. Convert it into the Celsius scale and the Kelvin scale.
Given Data
T_F = 98.6 °F
To Find
T_C
T_K
Formulas
T_C = (T_F − 32) ÷ 1.8
T_K = T_C + 273
Calculation
T_C = (98.6 − 32) ÷ 1.8 = 66.6 ÷ 1.8 = 37 °C.
T_K = 37 + 273 = 310 K.
Result
T_C = 37 °C; T_K = 310 K
Numerical 7.2
At what temperature would the Celsius and Fahrenheit thermometer readings be the same?
Given Data
T_C = T_F = T
To Find
T
Formula
T_F = 1.8 T_C + 32
Calculation
Put T_F = T_C = T: T = 1.8T + 32.
T − 1.8T = 32, so −0.8T = 32.
T = 32 ÷ (−0.8) = −40.
Result
T = −40 (−40 °C = −40 °F)
Numerical 7.3
Convert 5 °F to the Celsius and Kelvin scales.
Given Data
T_F = 5 °F
To Find
T_C
T_K
Formulas
T_C = (T_F − 32) ÷ 1.8
T_K = T_C + 273
Calculation
T_C = (5 − 32) ÷ 1.8 = −27 ÷ 1.8 = −15 °C.
T_K = −15 + 273 = 258 K.
Result
T_C = −15 °C; T_K = 258 K
Numerical 7.4
What is the equivalent temperature of 25 °C on the Fahrenheit and Kelvin scales?
Given Data
T_C = 25 °C
To Find
T_F
T_K
Formulas
T_F = 1.8 T_C + 32
T_K = T_C + 273
Calculation
T_F = 1.8 × 25 + 32 = 45 + 32 = 77 °F.
T_K = 25 + 273 = 298 K.
Result
T_F = 77 °F; T_K = 298 K
Numerical 7.5
The ice and steam points on an ungraduated thermometer are found to be 192 mm apart. What temperature will be on the Celsius scale if the length of the mercury thread is 67.2 mm above the ice point mark?
L = 192 mm from ice point to steam point; the thread is l = 67.2 mm above the ice point.
Given Data
distance between fixed points L = 192 mm
length above the ice point l = 67.2 mm
To Find
Temperature T_C
Formula
T_C = (l ÷ L) × 100
Calculation
T_C = (67.2 ÷ 192) × 100.
67.2 ÷ 192 = 0.35, so T_C = 35 °C.
Result
T_C = 35 °C
Note: Both lengths are in mm, so there is no need to change units: only their ratio matters.
Numerical 7.6
The length between the fixed points of a 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?
L = 20 cm between the fixed points; the mercury is l = 4.5 cm above the lower mark.
Given Data
L = 20 cm
l = 4.5 cm
To Find
Temperature T_F
Formulas
T_C = (l ÷ L) × 100
T_F = 1.8 T_C + 32
Calculation
T_C = (4.5 ÷ 20) × 100 = 22.5 °C.
T_F = 1.8 × 22.5 + 32 = 40.5 + 32 = 72.5 °F.
Result
T_F = 72.5 °F
Note: Directly on the Fahrenheit scale: T_F = 32 + (4.5 ÷ 20) × 180 = 32 + 40.5 = 72.5 °F, the same answer.
