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Two vectors are given: π‘₯βƒ— = 3𝑖⃗ + 2𝑗⃗, 𝑦⃗ = 2𝑖⃗ βˆ’ 8𝑗⃗.


a) Draw these vectors in Cartesian coordinate system.


b) Represent both of these vectors in magnitude, direction notation.


c) Represent vector 2π‘₯βƒ— + 3𝑦⃗ in magnitude, direction notation.

In a dentist's office an X-ray of a tooth is taken using X-rays that have a frequency of 6.30 x 1018Β Hz. What is the wavelength in vacuum of these X-rays?


An object is placed in front of spherical mirror, and the magnification of the system is m = -6. What does this number tell you about the image?



An engine operates between 1,200oC (T2) and

200oC (T1), and Step 1 (isothermal expansion) involves an expansion from 6x10-5Nm-2 to

4x104Nm-2. The working substance is one mole of an ideal gas.

i. Calculate the efficiency of the heat engine.

ii. Calculate heat absorbed in Step 1.

iii. Calculate the amount of heat rejected in Step 3 (isothermal compression). [5marks]

Fig 1:


The equilibrium freezing point of water is 0oC. At that temperature the latent heat of fusion of

ice (the heat required to melt the ice) is 6063J/mol.

i. What is the entropy of fusion of ice at 0oC? [3 marks]

ii. What is the change of Gibbs free energy for ice water at 0oC? [1 mark]

iii. Repeat parts (i) and (ii) at -5oC [4marks]


At -5oC, the vapour pressure of ice is 3.012mmHg and that of super cooled liquid water is

3.163mmHg. The latent heat of fusion of ice is 5.85kJ/mol at -5oC.

Calculate Ξ”G and Ξ”S per mole for the transition of from water to ice at -5oC. [4 marks]


Calculate the velocity of longitudinal waves in mercury if the bulk modulus of mercury is 2.6 x 10 Exp. 11 dynes/sq.cm and its density is 2,000,000 dynes.Β 




Suppose the radius is measured to be r=6.0cm+-0.1cm





a,the true value of the radius lies between _





b,what is the significant figure of area

One sometimes speaks of the β€œdirection of time”, evolving from past to future. Does this mean that time is a vector quantity


. The temperature of an ideal gas increases from 20 ̊C to 40 ̊C while the pressure stays the same. What happens to the volume of the gas?


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