Thermal Properties of Matter

Sponsor Area

Question
CBSEENPH11020369

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the following figure. 

Solution

B.

We know that dQ over dt space equals space KA dθ over dx
In steady state flow of heat
dθ space equals space dQ over dt.1 over KA. dx
rightwards double arrow straight theta subscript straight H space equals straight theta space equals space straight k apostrophe straight x
rightwards double arrow space straight theta space equals straight theta subscript straight H space minus space straight k apostrophe straight x
Equation space straight theta space equals space straight theta subscript straight H space minus space straight k apostrophe space straight x space represents space straight a space straight space line

Sponsor Area

Question
CBSEENPH11020393

One end of a thermally insulated rod is kept at a temperature T1 and the other at T2. The rod is composed of two sections of lengths

  • (k2

  • (k2

  • (k1

  • (k1A1 T1 + k2A2T2) / (k1A1 + k2A2)

Solution

C.

(k1 fraction numerator left parenthesis straight T subscript 1 minus straight T right parenthesis straight k subscript 1 over denominator calligraphic l subscript 1 end fraction space equals space fraction numerator left parenthesis straight T minus straight T subscript 2 right parenthesis straight k subscript 2 over denominator calligraphic l subscript 2 end fraction
straight T space equals space fraction numerator straight T subscript 1 straight k subscript 1 calligraphic l subscript 2 space plus space straight T subscript 2 straight k subscript 2 calligraphic l subscript 1 over denominator straight k subscript 1 calligraphic l subscript 2 space plus straight k subscript 2 calligraphic l subscript 1 end fraction

Question
CBSEENPH11020394

If Cp and Cv denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

  • Cp – Cv = R/28

  • Cp −Cv = R/14

  • Cp −Cv = R

  • Cp – Cv = 28 R

Solution

A.

Cp – Cv = R/28

Question
CBSEENPH11020412

Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on Earth, at a distance r from the Sun.

where r0 is the radius of the Earth and σ is Stefan’s constant

  • fraction numerator straight R squared σT to the power of 4 over denominator straight r squared end fraction
  • fraction numerator 4 πr subscript 0 superscript 2 straight R squared σT to the power of 4 over denominator straight r squared end fraction
  • fraction numerator πr subscript 0 superscript 2 straight R squared σT to the power of 4 over denominator straight r squared end fraction
  • fraction numerator straight r subscript 0 superscript 2 straight R squared σT to the power of 4 over denominator 4 πr squared end fraction

Solution

C.

fraction numerator πr subscript 0 superscript 2 straight R squared σT to the power of 4 over denominator straight r squared end fraction